Skip to main content

Full text of "Papert Seymour-The Children's Machine.pdf (PDFy mirror)"

See other formats

Library of Congress Cautoging-in-Pubiication Data 

Papert, Seymour. 

The children's machine: rethinking school in the age ot the 

computer/Seymour Papert. 

p. cm. 

Includes bibliographical references (p. ) and index. 
ISBN 0-465-0183O-0 

1. Computer assisted instruction. 2. Education— Data processing. 
I. Tide. 

LB1028.5.P325 1992 

371.3'34-dc20 91 "^ 12 

Copyright © 1993 by Seymour Papert. Published by Basic-Books. A 
Division of HarperCollins Publishers, Inc. 

All rights reserved. Printed in the United States of America. No part of 
this book may be reproduced in any manner whatsoever without wntten 
permission except in the case of brief quotations embodied in cntical 
articles and reviews. For information, address BasicBooks, 10 East 53rd 
Street, New York, NY 10022-5299- 

Designed by Ellen Levine 

93 94 95 96 CC/HC 987654321 

• • • 

Preface vit 

Acknowledgments xi 

1 Yeamers and Schoolers * 

/2 Personal Thinking 22 

/ 3 School: Change and Resistance to Change 35 

\ 4 Teachers 57 

3 A Word for Learning 82 

6 An Anthology of Learning Stories 106 

7 Instructionism versus Constructionism 137 
0) Computerists 157 

A fl9J Cybernetics ^9 

10 What Can Be Done? 205 

Sources of Information 227 

Bibliography 229 

Yearners and 

IMAGINE a party of time travelers from an earlier century, 
among them one group of surgeons and another of school- 
teachers, each group eager to see how much things have 
changed in their profession a hundred or more years into the 
future. Imagine the bewilderment of the surgeons finding them- 
selves in the operating room of a modern hospital. Although they 
would know that an operation of some sort was being performed, 
and might even be able to guess at the target organ, they would 
in almost all cases be unable to figure out what the surgeon was 
trying to accomplish or what was the purpose of the many strange 
devices he and the surgical staff were employing. The rituals of 
antisepsis and anesthesia, the beeping electronics, and even the 
bright lights, all so familiar to television audiences, would be 
utterly unfamiliar to them. 

The time-traveling teachers would respond very differendy to a 
modern elementary school classroom. They might be puzzled by 
a few strange objects. They might notice that some standard tech- 
niques had changed — and would likely disagree among them- 
selves about whether the changes they saw were for the better or 
the worse — but they would fully see the point of most of what 

2 • The Children's Machine 

was bein^empted and could quite easily take over the das, I 
use this^Lto provide a rough-and-ready 
unevenneWprogress across the broad front of ta-anad 
change. In the wake of the startling growth of science and techno 
ogy in our recent past, some areas of human activity have unde, 
gfne megachange. Telecommunications, entertainm and 
Lsportation, as well as medicine, are among them. School* a 
notabTe example of an area that has not. One cannot ******* 
has been no change at all in the way we dish out educate ^ou 
students. Of course there has; the parable gives me a way ot 
pointing out what most of us know about our system of school- 
ing: Ye" it has changed, but not in ways that have =substant^ 
/altered its nature. The parable sets up the quesuon: Why, through 
tZZi when so much human activity has been revoluuon^d 
have we not seen comparable change in the way we help our 

\children learn? . . 

I have posed this question in situations ranging from casual 
conversation to formal seminars, and with audiences 
children who have had only a few years of contact with S hool to 
professional educators who have spent a lifetime in it. Although 
w L answers I have received are as varied as the expected range of 
$ e ponses to a Rorschach inkblot test, the distribution is far from 
f even from one extreme to the other. Most fall on one side or the 

other of a great divide. 

' > People on one side, thefhc^, are taken aback by my 

question, surprised that I se%^ looking * 
They acknowledge that Scho^T has problems (who doesnt 
today?) and are very concerned about solving them. But mega- 
change? What can you possibly mean? 

Many become indignant. Talking about megachange feels to 
them like fiddling while Rome burns. Education today is faced 
with immediate, urgent problems. Tell us how to use your com- 
puters to solve some of the many immediate pracucal problems 

we have, they say. 

On the other side of the great divide are the/>5Df*fK, who 

Yearners and Schoolers • 3 

respond by citing impediments to change in education such as 
cost, politics, the immense power of the vested interests of school 
bureaucrats, or the lack of scientific research on new forms of 
learning. These people do not say, "I can't imagine what you 
could possibly be looking for," because they have themselves felt 
the yearning for something different. 

Many individual Yearners — frojn^paients toteachers to ad- 
ministrators — simpiyjfmd^^ particularly 
when they find School's problems directiy constraining their aspi- 
rations for their own children. Some parents keep their children at 
home: There are several hundred thousand hojnejchijojers in the 
United States. Others actively seek out alternative schools or even 
help to create schools that offer such alternatives. 

Another important class of Yearners operates as a sort of fifth 
column within School itself: Large numbers of t eache rs manage to 
create within the walls of their own classrooms oases of learning 
profoundly at odds with the education philosophy publicly es- 
poused by their administrators; some public school districts, per- 
haps those where Yearners have moved into administration, have 
made space for Yearners within School by allowing for the estab- 
lishment of alternative programs within the School system, allow- 
ing such programs to deviate from district policies on method and 

But despite the many manifestations of a widespread desire for 
something different, the education establishment, including most 
of its research community, remains largely committed to the edu- 
cational philosophy of the late nineteenth and early twentieth 
centuries, and so far none of those who challenge these hallowed 
traditions has been able to loosen the hold of the educational 
establishment on how children are taught. 

The time-traveling teachers of my parable who saw nothing in 
the modern classroom they did not recognize would have found 
many surprises had they simply gone home with one or two of the 
students. For there they would have found that with an industri- 
ousness and eagerness that School can seldom generate, many of 

4 • The Children's Machine 

t he students had become intensely involved in teaming therute 
and strategies of what appeared at finance to be a process 
much more demanding than any ho^^gnment The stu- 
f dents would define the subject as^eojar^nd what they 

I were doing as &ay) — , t niir 

V while the teSology itself might first catch the eye of ou 
visitors, they would in time, being teachers, be struck by the level 
of intellectual effort that the children were putting into this activity 
/and d^eyelofjea^^ 

|\ S^oKTmo^^ and honest of^urlm^ra7eling teachers 
5gTu well observe that never before had they seen so much bemg 
learned in such a confined space and in so short a time. 

School would have parents-who honestly don't know how 
to interpret their children's obvious love affair with video 
games-believe that children love them and dislike homework 
fec^fse the first is easy and the second hard. In reality, the reverse 
is more often true. Any adult who thinks these games are easy 
|f need only sit down and try to master one. Most are hard, with 
complex information-as well as techniques-to be mastered 
the information often much more difficult and ume consuming to 
master than the technique. 
* If that argument did not convince parents that the games are 
not serious, surely a second argument would: Video games are 
toys -electronic toys, no doubt, but toys-and of course chil- 
dren like toys better than homework. By definition, play is enter- 
ing, homework is not. What some parents may not realize, 
//however, is that video games, being the first example of computer 
f technology applied to toy making, have nonetheless been the 
entryway for children into the world of computers. These toys, by 
empowering children to test out ideas about working within pre- 
fixed rules and structures in a way few other toys are capable of 
doing, have proved capable of teaching students about the possi- 
\ bilities and drawbacks of a newly presented system in ways many 
1 adults should envy. 

Yeamers and Schoolers • 5 

Video games teach children what computers are beginning to 
teach adults — th at some forms of learning are fast-paced, im- 
mens ely compel ling, and rewarding. The fact that they are enor- 
"mousTy demanding of one's time~and require new ways of think- 
ing remains a small price to pay (and is perhaps even an 
advantage) to be vaulted into the future. Not surprisingly, by^ 
comparison School strikes many young people as slow, boring, 
and frankly out of touch. 

The introduction of computers is not the first challenge to 
education values. For example, John Dewey began his campaign 
for a more active and self-directed style of learning in schools over 
a hundred years ago, and in these intervening years numerous 
more or less radical reformers have strived to change School. Back 
then Dewey undertook his formidable task armed with little more 
than a strong philosophical sense about the way children develop, 
for at the time there was no strong movement from society in 
general for change in schools. There was certainly no dissatisfac- 
tion with education in Dewey's time as strong as the current one, 
which seems at times willing to accept the virtual destruction 
of the public school system rather than have things continue as 
they now are. Dewey remains a hero to those who believe in a 
twentieth-century vision of a child as a person with the right to 
intellectual self-determination, and there can be little doubt that a 
child treated with respect and encouragement rather than threat- 
ened with rejection and punishment will fare better under any 
system of education. But while Dewey's influence has surely 
removed some of the crudest impediments to the healthy devel- 
opment of the child, it has been so diluted that it barely addresses 
the next serious question: In trying to teach children what adults 
want them to know, d oes School utilize the way human bein gs 
most n^j jrai^ lea rn in _nonschool settings? 

The failure of past reformers to bring about dramatically better 
learning has armed those within the educational establishment 
with the argument that future proposals will prove no more capa- 
ble of bringing about radically improved learning. Some may well 

.6 • The Children's Machine 

believe that the best argument against megachange is this: tfft has 
„ not caught fire But tne feehngs of 

LTnt/ ch1*ea' .n ,he pas, children may no, have £d 

very long beyond the time when children can no longer be per 

evelt — as Dewey, .he comparer, <-«™ 
manifestations, is offering rhe Vearners new 

tives be createu u rh anae first enhance the lives 

sa. . - - 

wit h mnch effon ffnd Us way ^^^^Snowtog 

change in public elementary schools. Most of the examples I us 
will be reaLcally^estJnjcale. They are offered not as exact 
«S^^n intimation of the rich poten- 
tial thl the future might hold. The following story, pan fact and 

The factual pan involves an encounter I had with a four-year 
old preschooler. Jennifer heard that I had grown up in Afnca and 

Yeamers and Schoolers • 7 

asked me whether I knew how giraffes sleep. "They have such 
long necks," she said, and wondered where they put their heads 
when they rest. 1 said (truthfully) that I didn't know, and asked 
what she thought. She explained her problem with a gesture of 
cozying her head in folded arms: "My dog cuddles her head when 
she sleeps and so do I, but the giraffe's head is so far away." I 
pursued the conversation with other children who joined us, and 
gleaned a bumper crop of good theories. One suggested that the 
giraffe sleeps standing up "like a horse." This set off an animated 
discussion, which kept coming back to the question of where the 
animal puts its head. No one offered that the head might stay up 
high. Someone said it can put its head on the ground if it does a 
split. Jennifer, who had moved over to the idea of their sleeping 
standing up, showed obvious delight when she hit on a theory: "It 
finds a tree with a branch for its neck." I asked what would 
happen if there were no tree. She looked at me disdainfully and 
informed me that of course there would be trees — giraffes eat the 
tops of trees, that's why they have such long necks. 

In this conversation we see two sides of the intellectual life of 
children of this age: the coexistence of a remarkable capacity for 
making theories with a nearly helpless dependence on adults for 
information that will test the theories or otherwise bring them 
into contact with reality. Jennifer is in a stage of transition. 
Younger children are more completely engrossed by a world 
within the range of immediate exploration. At a later age, unless, 
as too often happens, the spirit of inquiry has been extin- 
guished, they will be able to explore a world beyond touch and 

Back in my own home that evening, still stimulated by my talk 
with the children, 1 threw myself into an exploration of giraffes 
with the intensity and perhaps even the immediacy of Jennifer's 
interactions with her puppy. I do not keep a pet giraffe, but I do 
have a library of books, of which quite a few were soon strewn all 
over my work area as I continued, with diversions en route, a 
rewarding chase after information about the sleep habits of 

8 • The Children's Machine 

giraffes. I was able to explore this world because the books gave 
me an extended immediacy. 
Until recendjcitj^l^ 

nef^cannoTread, oTe^Tif they can they would not be able 
^ to conduct that kind of search. But this answer is no longer 
/ n convincing. No technicalobstacle jundstaAe way of making a 
machine^ let's call it tgKn^SfeMa^-that would put 
the power to know what others know into jenmfer^iiand^ It is 
almost twenty years since my MIT colleague Ni^Ne^Jonte 
built a machine that allowed the vicarious exploWo^re small 
v town of Aspen, Colorado, through a computer. Extremely pnmi- 
>tive examples are now trickling into commercial production under 
\<^> names like "interactive video" or electronic book, "ebook or 
** / ,- "GDI," or, in slightly more elaborate versions, "virtual reality. 
//V^ What separates these endeavors from a true Knowledge Ma- 
^ chine is no longer a lack of storage or access technology but the 

^ size of the effort ngededtobring together thejtnoYvjedge. But the 
^ * e^r^uTp^tia^^ makes ltS 

\jP eventual appearance inevitable. 

• Such a system would enable a Jennifer of the future to explore 

a world significantly richer than what I was offered by my printed 
books. Using speech, touch, or gestures, she would steer the 
machine to the topic of interest, quickly navigating through a 
knowledge space much broader than the contents of any printed 
encyclopedia. Whether she is interested in giraffes or panthers or 
fleas, whether she wants to see them eating, sleeping, walking, 
running, jumping, fighting, birth ing, or copu lating, she would be 
able to find her way to the relevant sounds and images she be- 
lieves would help her understand what she wants to understand 
Though nothing in my argument here depends on it, this availabil- 
ity will one day be extended to experiencing the very smell and 
touch and maybe the kinesthesia of being with the animals. 

The Knowledge Machine so described barely scratches the sur- 
face of how new media will change children's relationships with 
knowledge. But even the most superficial considerauon of this 

Yearners and Schoolers • 9 

question requires one elemental but consequential concession: 

Children who grow up with the opportunity to explore the jungles^ s^f*^ 

and the cities and the deep oceans and ancient myths and outer 
space will be even less likely than the players of video games to 
sit quietly through anything even vaguely resembling the 
elementary-school curriculum as we have known it up to now! j 

A less superficial consideration leads one to ask: How would 
the introduction of Knowledge Machines into the School envi- 
ronment compromise the primacy with which we view reading 
and writing — that is, children's fluency in using the alphabetic 

In the literature on education there has long been a pervasive 
tendency to a ssume that rea ding is the principal access route to 
k nowledge for student s. Someone who cannot read is said to be 
doomed to ignorance, or at least to dependence on that limited 
amount of important information that can be obtained orally. 

The educational development of children is therefore seen as 
rigidly dependent on learning to read in a timely way. The pros- 
pect of the Knowledge Machine suggests that this basic assump- 
tion may not necessarily be true for all time, and indeed may start 
to unravel within a decade or two. I am not suggesting that the 
written language is likely to be abandoned. I am suggesting that 
new thinking is needed about the position assigned to it as the 
prerequisite to the accumulation by students of useful knowledge, 
or at least as the first route to be opened to children when they 
begin their formal educations. 

I have even firmer convictions about another kind of issue 
raised by the Knowledge Machine and the primacy of reading in 
our present culture as the essential route to knowledge. Learning 
to read and write is an important part of what is happening to 
Jennifer in the first grade, but it is not necessarily at the core of 
what is being communicated to her about what learning is all 
about. Jennifer's transition is really epistemic; although she is 
totally unaware of it, sh e is bg jng_siiif te d from r eliance on o ne 
dominant way of kno win g to reliance on another. 

As an infant she acquired knowledge baffxploratioh,. She was 

10 • The Children's Machine 

in charge of her jearning . Though her parents put knowledge in 
heTpath, she chosTPsvTiat she would investigate, determining for 
herself what she would think about and how she would think 
about it. This is not to say that adults did not try to a lesser or 
greater extent to control her and her learning. But it is well docu- 
mented that preschoolers do not deposit the knowledge adults try 
to feed them in their memory banks in the same way they learn to 
do later on, when they go to school. It is metabolized, assimilated 
with all their other direct experiences of the world. 

When Jennifer asked me about the giraffe, however, she was at 
a stage when more questions were coming up in her mind than 
she could answer by direct exploration of her immediate world. 

ae responded in a way she had been taught to respond: Ask a 
apathetic adult who would reward her curiosity with praise. 
While pressure toward this mode of learning — by being told, by 
accepting authority — has its roots in a student's own curiosity, it 
will in the course of the educational experience of most children 
be massively reinforced by School. Where Jennifer will come out 
in the end will depend on many social, psychological, and acci- 
dental factors. What is clear is that she is entering a period of 
transition that will have a profound and perhaps brutal and dan- 
gerous impact on her intellectual development. Common School 
parlance often uses the word literacy to refer to the state of being 
able to read and write. Howevei vthinkers wh o try to look more 
deeply int o what education means have wr itten scathinglv_m_criti- 
cism of the idea tha t illiteracy can be remeaUedj 3yjeacjting_ch^- 
drenthe mechanical skill of decoding black marks on white re aper. 
Much~more is invoTve^rPaT3toTreire"enjoins us not to dissociate 
"reading the word" from "reading the world." Becoming literate 
means thinking differently than one did previously, seeing the 
world differently, and this suggests that there are many different 

In this sense, the choice of name for the process becomes 
epistemological; writers have more recently suggested as substi- 
tutes for this literacy the term ways of knowing, I am entirely in 

Yearners and Schoolers • 11 

sympathy with the intentions of these writers but feel deprived of 
a word for the distinction between a literal sense of literacy and 
the various more sophisticated senses the idea evokes. 

In desperation I have coined the words letteracy and letterate 
to refer to the special skill involved in reading words made up of 
alphabetical letters. Outside this more narrow definition will re- 
main the opportunities, offered for the most part by the new 
media represented symbolically by the Knowledge Machine, al- 
lowing students to become highly literate independent of their 
progress toward letteracy. 

The need for such linguistic maneuvers reflects the radical 
nature of the revolution in media introduced by the computer. 
Without risk of serious oversimplification one can say that 
there have been, up to now, two widely used media for the 
transmission of information and ideas and only one major histori- 
cal transition. 

For most of human history speech stood alone as the trans- 
mitter of what had previously been learned. Drawings, smoke 
signals, and gestures were important supplements to speech but 
never threatened the monopoly of speech in determining what 
information people in any society would share, group to group or 
even generation to generation. Writing was the first significant 
departure from the oral tradition, and whether the emergence of 
written language dates back to Egyptian hieroglyphics or Guten- 
berg is a matter of detail. 

Filmmakers, painters, and other users of evolving media may be 
slighted by my decision to count computer-based media as the 
next substantive advance. But I think that Jennifer's story captures 
better than abstract words an important aspect of what makes the 
new media qualitatively different. It especially makes clear by 
showing us an alternative to the risk children are placed in by the 
fact that literacy and letteracy are virtually synonymous. They are 
at risk because they do not have access to a wider immediacy for 
exploration and have only very limited sources to which they can 
address questions. They are doubly at risk because the situation 

12 • The Children's Machine 

consolidates School in its traditional role of imposing letteracy and 
all the rigidity that goes with that role. 

It is not surprising, given the newness of this technology, that 
we have developed no universally accepted language to use in 
talking about it. ^ rhu not mean that we should be un- 
aware that a revolution is in the making, or thjuwe should_ noldp 
eve mhlnipcSEIo guide its^ deydojament. For in regard to the 
questions of how to reform elementary education, the movement 
from letteracy to media-based knowledge acquisition may be even 
more important than the movement from preletterate to letterate 

It is important to remember that the letteracy revolution (that is 
to say, the advent of writing and printing) did not directly touch 
the primary ways in which most two- or four- or even six-year- 
olds explore the world and learn about it. Of course, the really big 
questions about the future of literacy and letteracy are beyond the 
scope of this book. But what is important here is that the Knowl- 
edge Machine offers children a transition between preschool 
learning and true literacy in a way that is more personal, more 
negotiational, more gradual, and so less precarious than the 
abrupt transition we now ask children to make as they move from 
learning through direct experience to using the printed word as 
the source of important information. 

Why, then, would anyone fail to take seriously, as Schoolers do, 
something that could be so consequential for the educational 
process? Willfulness? A stubborn refusal to abandon old ways? 
These factors are present in any challenge to long-established 
procedures. The problem in education has an additional element. 
(Most honest Schoolers are locked into the assumption that 
School's way is the only way because they have never seen or 
imagined convincing alternatives in the ability to impart certain 
nets of knowledge. 

Even the most confirmed Schooler will readily concede that 
some important learning happens very successfully under condi- 
tions very different from School: Babies learn to talk without 



Yearners and Schoolers • 13 

curriculum or formal lessons; people develop skill at hobbies 
without teachers; social behavior is picked up other than through 
classroom instruction. A Schooler might grant that a Knowledge 
Machine could extend the scope of such learning to include far- 
away giraffes as well as nearby puppies, but still be worried by n ot 
having heardjnfjmvone. exce pt perhaps some highly gifted e x- 
c eptions, who managed to become learned in such difficult disci - 
plines asjTeorpetr y or al gebra through other than well-established 
and time-tested educational programs of instruction. 

These skeptics have no trouble imagining, for example, a 
teacher leading a class of students by "Socratic questions" to 
"discover for themselves" some formula in mathematics. But they 
don't see this as significantly different than a good explanation of 
the formula. I have to agree with them. Although I have always 
yearned for ways of learning in which children act as creators 
rather than consumers of knowledge, the methods that have been 
proposed have always seemed to me marginally superior, if at all, 
to the old ways. 

A turning point came for me in the early 1960s, when comput- 
ers changed the fabric of my own work. What struck me most 
forcibly was that certain problems that had been abstract and hard 
to grasp became concrete and transparent, and certain projects 
that had seemed interesting but too complex to undertake became 
manageable. A t the same time I had mv first experience of t he 
excitement and the holding power that keeps people working a ll 
n ight with their computers. I realized that children might be able 
to en j oy the same advantages — a thought that changed my l ife. 

My goal became to strive to create an environment in which all 
children— whatever their culture, gender, or personality— could 
learn algebra and geometry and spelling and history in ways more 
like the informal learning of the unschooled toddler or the excep- 
tional child than the educational process followed in schools. 
Stated in the language of the skeptical Schooler, my driving ques- 
tion was whether "exceptional children" learned differently be- 
cause they were exceptional or whether, as I suspected, they 

14 • The Children's Machine 

became exceptional because circumstances allowed them to learn 

1 can hear many Schoolers saying to themselves as they read 
this: "Yes, yes, we've heard that before. It's the old refrain of 
progressive education. That's been tried and it didn't work. You 
yourself have just poked fun at the discovery method in algebra." 

There is a family resemblance (and I shall accept the word 
progressive to name it) between the vision of learning I am pre- 
senting here and certain philosophical principles expressed in the 
diverse forms of innovations that go under such names as progres- 
sive or open or child-centered or constructivist or radical educa- 
tion. I certainly share with this broad movement the criticism of 
/•School as casjiftg-the child in the role of passive recipient of 
* knowledge. 'P^uloF^ire expresses the criticism most vividly in his 
description of !knool as following a "banking model" in which 
information is deposited in the child's mind like money in a sav- 
ings account. Other writers express the same thought by accusing 
School of treating the child's mind as a "vessel to be filled" or as 
the receiver at the end of a transmission line. 

One way in which I am at variance with progressive education 
becomes apparent when we turn from criticizing School to invent- 
ing new methods. In my view almost all experiments purporting 
to implement progressive education have been disappointing be- 
cause they simply did not go far enough in making the student the 
subject of the process rather than the object. In some cases this 
came about because the experimenters were too timid; thj^experi- 
mentsfailed just as the test o f a n y medica l, t i rarmpnr would jail if 
the treaOog-jiojCtojr^ 

In most cases there were reasons deeper than timidity in hold- 
ing them back. Early designers of experiments in progressive edu- 
cation lacked the tools that would allow them to create new meth- 
ods in a reliable and systematic fashion. With very limited means 
at their disposal, they were forced to rely too heavily on the 
specific talents of individual teachers or a specific match with a 

Yearners and Schoolers • 1 5 

particular social context. As a result, what successes they had often 
could not be generalized. 

Another parable will emphasize this point and also clarify 
where I see my main new contribution to the old debate. My 
hypothetical Schoolers said that progressive education has been 
tried and did not work. I agree that it hasn't worked very well — 
but in something like the sense in which Leonardo da Vinci failed 
in his attempts to invent an airplane. Making an airplane in Leo- 
nardo's time needed more than a creative manipulation of all that 
was known about aeronautics. His failure to make a workable 
airplane did not prove him wrong in his assumptions about the 
feasibility of flying machines. 

Leonardo's airplane had to wait for the development of some- 
thing that could come about only through great changes in the 
way society managed its resources. The Wright Brothers could 
succeed where Leonardo could only dream because a technologi- 
cal infrastructure supplied materials and tools and engines and 
fuels, while a scientific culture (which developed in coevolution 
with this infrastructure) supplied ideas that drew on the peculiar 
capabilities of these new resources. 

Educational innovators even in the very recent past were in a 
situation analogous to Leonardo's. They could and did formulate 
bold perspectives: for example, John Dewey's idea that children 
would learn better if learning were truly a part of living experi- 
ence; or Freire's idea that they would learn better if they were 
truly in charge of their own learning processes; or Jean Piaget's 
idea that intelligence emerges from an evolutionary process in 
which many factors must have time to find their equilibrium; or 
Lev Vygotsky's idea that conversation plays a crucial role in 
learning. Such ideas have always appealed to Yearners; they res- 
onate with a respectful attitude toward children and a demo- 
cratic social philosophy. 

Sadly, in practice they just wouldn't fly. When educators tried 
to craft an actual school based on these general principles, it was 
as if Leonardo had tried to make an airplane out of oak and power 

16 • The Children's Machine 

it with a mule. Most practitioners who tried to follow the seminal 
thinkers in education were forced to compromise so deeply that 
the original intent was lost. For example, the -discovery method" 
may take a step in the direction of Dewey's dream, but it is a 
minuscule step, utterly insufficient to make the kind of difference 
expressed in the grand vision of empowered children learning 
through living experience. It is simply double-talk to ask children 
to take charge of their own learning and at the same time order 
them to "discover" something that can have no role in helping 
them understand anything they care about or are interested in or 
curious about. 

As a mode of access to knowledge of the kind Jennifer was 
seeking, the machine will not be more than a suggestive metaphor 
for some time yet to come because the quantity of factual knowl- 
edge needed to make it work is so vast. But there are other areas 
of knowledge where the epistemic transition is even more brutal 
for many children, and where a machine that will provide a con- 
tej£-forsoftening it is very much closer at hand. One such area is 

N^Jfjheiciea of a transition from oral to letterate ways of knowing 
seems less applicable to mathematics, this is largely because our 
culture is inclined to reserve the name mathematics for the letter- 
ate kind of mathematics taught in school and perhaps a minimal 
intuitive basis directly connected with it. But by closing off a much 
larger basis of knowledge that should serve as a foundation for 
formal mathematics, we have cut off the route to better learning. 
Every preschool child has amassed on his or her own special 
mathematical knowledge about quantities, about space, about the 
reliability of various reasoning processes, elements that will be 
useful later in the math class. The enormous quantity of this "oral" 
mathematics constructed and retained by every child has been 
well documented by Jean Piaget. 

The central problem for math education is to find ways to draw 
on the child's vast experience of oral mathematics. Computers can 
do this. 

Yeamers and Schoolers • 17 

The most powerful use made of computers in changing the 
epistemological structure of children's learning to date has been 
the construction of micro worlds, in which children pursue mathe- 
matical activity because the world into which they are drawn 
requires that they develop particular mathematical skills. Simulta- 
neously, these worlds match in form the successful oral style of 
young children's learning. Giving children the opportunity to 
learn and use mathematics in a nonformalized way of knowing 
encourages rather than inhibits the eventual adoption of a formal- 
ized way as well, just as the Knowledge Machine, rather than 
discouraging reading, would eventually stimulate children to read. 

In saying this I must emphasize a difference with many trends 
in the use of concrete or constructivist methods to teach math. The 
entire point of the Knowledge Machine would be lost if it were 
conceived solely as a device for teaching children to read. Simi- 
larly, the point of developing nonformalized ways of knowing in 
mathematics is entirely subverted if these are conceived as a scaf- _ t 
folding for learning the formal way or as a trick to lure children "* 
into formalized instruction. They have to be valued for themselves \ .^r^^ 
and genuinely useful to the learner in and of themselves. Many / 
more examples of this distinction will be found in later chapters. 

Here I make the point simply by looking at the original design (j& 
on the next page that was made (in magnificent color, which 
unfortunately cannot be reproduced here) by children in a New 
York City middle school as part of a study of African textiles. The 
design was made by programming a computer in the program- 
ming language Logo using a nonformalized version of a kind of 
mathematics called turtle geometry. These students did not use 
the design process in order to learn more formal geometry. They 
used a kind of geometry that matched their preferred way of 
knowing in order to pursue ideas about African design. Geometry 
is not there for being learned. It is there for being used. The main 
exception I would make is a big one: Both geometry and learning 
it can be objects of love, in which case use might fall by the 

18 • The Children's Machine 

The African textiles design. The drawing at right was also 
generated by children, using Logo to program computers in the 


Yearners and Schoolers • 19 

These remarks about formal and other geometries might be 
offensive to many Yearners as well as to most Schoolers. For I 
seem to be saying that some students should be satisfied with a 
kind of useful geometry other than the real McCoy, and this might 
be read as if it had an undertone of elitism. What I am really 
saying, and will develop particularly in chapter 9, is that there is 
room for much rethinking about what knowledge, and what ways 
of knowing, should have a privileged status. Certainly School has 
not earned the right to decide for us. Those Yearners who yearn 
for better ways to teach what School has decreed everyone should 
know have not quite accepted the idea of megachange. I hope, 
after reading this book, they will have moved toward questioning 
not only how School teaches but what as well. 

A bigger departure from the curriculum is shown by a project 
in which children invent and build artificial creatures using a 
version of Lego extended to include tiny computers, which take 
in information from sensors and control motors. The computer 
can be programmed in Logo to make the creatures move in a 
"purposeful" way. For example, an eight-year-old girl constructed 
a model "mother cat" and its "kitten." Both would roam until the 
kitten beeped and flashed a light mounted on its head; at this 

20 • The Children's Machine 

signal the cat would begin to move toward it. Other children have 
built snakes and monsters. One team built an "intelligent" model 
house that cleaned itself. 

The idea of programming such behavior might sound difficult. In 
fact, the latest user-friendly versions of Logo (such as Microworids 
Logo) make it so easy that technological construction and the 
underlying scientific principles become as natural a medium for 
the expression of fantasy as for drawing or speech. Thus one of the 
subject lines that splits School's epistemology is blurred: Tradition- 
ally in School, the art and writing classes might have time for fantasy, 
but science deals with facts. No wonder many children find it cold. 
A second subject line is blurred by the union of technology with 
biology. Making an artificial animal is no substitute for studying real 
ones, but it does provide insight into aspects of real animals, for 
example, the principle of "feedback" that enables the Lego cat to 
find its kitten. The situation is analogous to the way in which the 
principle of lift lies behind the flight of birds and airplanes, but there 
is a big difference in the social importance of the two cases. While it 
does not matter very much whether people understand lift, feed- 
back is a key concept for thinking about systems. The lack of ability 
to think fluently about the environment, the economy, or even 
one's family as a system matters very much indeed. 

The concept of feedback illustrates how artificial it is to confine 
science to the precisely stated kind of knowledge favored by 
letteracy. The Lego cat never "knows" at all precisely where the light 
is located; all it "knows" is vaguely whether it is more to the left or 
more to the right. The program makes the cat turn a little in the 
appropriate direction, move a little forward, and repeat the cycle; 
turning one degree or ten degrees on each round will work equally 
well. Thus, what the cat "knows" is more in tune with the qualitative 
knowledge of a preletterate child than with anything precise and 
quantitative. The fact that it can nevertheless find its way to the exact 
destination is empowering for all qualitative thinkers and especially 
for children. It allows them to enter science through a region where 
scientific thinking is most like their own thinking. 

Yearners and Schoolers • 21 

The idea that partial and qualitative knowledge can be good 
knowledge is applicable to a discussion of whether building a 
Lego model is really relevant to the scientific study of biology. If 
one rejects all inexact knowledge, one might believe that the only 
way a model can elucidate nature is by simulating it precisely. The 
model cat shows a different kind of simulation, a "soft simulation" 
that provides qualitative understanding of a complex system by 
constructing a simple one with which it shares a principle. 

The computer graphics and the artificial creature projects give 
a glimpse of directions of change for School that move toward 
megachange. The rest of this book is structured by three themes 
that bear on the likelihood of School actually doing so. The most 
down-to-earth of the three is a look at what is happening in 
schools. In chapter 3 I look at the response of School as an 
institution to the images of change I have anticipated here. Chap- 
ter 4 discusses teachers and chapter 10 discusses issues of strategy 
for change. The next theme is directed at developing a better 
sense of the evolution of the technology itself and the ideas and 
cultures that have come with it. This discussion permeates the 
entire book but is specifically focused in c hapters J Lartd-g. The 
final theme is the most controversial. I believe that if we are to 
have new forms of learning, we need a very different kind of 
theory of learning. The theories that have been developed by 
educational psychologists, and by academic psychologists in gen- 
eral, are matched to a specific kind of learning, School's kind. As 
long as these ways of thinking about learning remain dominant, 
it will be very hard to make a serious shift from the traditional form 
of School. 

In the next chapter I give a first view of the direction in which 
I would look in order to find new ways of thinking. In its briefest 
description, this direction is within o urgskes. In chapter 5 I pro- 
pose giving a name to a new kind of theory of learning which will 
reflect the fact that human experience gives all of us a vaster store 
of knowledge about learning than has been accumulated by all 
the white-coated academics injheir laboratories. 

Personal Thinking 

A course on psychology I took as an undergraduate left 
little residue in my mind, except for a homily on objectiv- 
ity delivered in the first lecture. We were warned that 
many of us might have enrolled under the erroneous impression 
that the course, being about psychology, would provide an occa- 
sion to explore the psychological issues in our own lives Those 
who had come for this reason were advised to consider whether 
they really wanted to be there. The starting point for the study of 
scientific psychology was, we were told, the skill of distancing 
oneself from the object of study. We would have to work hard to 
learn how to keep intuitions based on our own experiences out of 
our thinking about the psychological issues we would be studying 
Without a doubt there is a need in any discipline for skill in 
distancing oneself from the object of study. However, the more 
significant lack in the study of education is quite the opposite- 
There is too much distancing. 

Yearners have tirelessly protested the way that School's curricu- 
lum distances knowledge from the individuality of the student 
Beyond this, the quest for a science of education has led to ways 
of thinking about teaching that exclude the teacher as a person 

Personal Thinking • 23 

and ways of thinking about education research that exclude the 
researcher as a person. My protest starts by situating my own work 
on educational innovation in my life experience. 

My critique of School and yearning for something else began very 
early. In elementary school I already knew quite clearly thatmv 
b est intellectual work was done outside the classroom. My rese n 
ment of Schoor wa s mitigated only by the fact that I lov ed tw 
tea^hersa ndThad a h andful of frimos who participated with jr 
in acJivifesJ^considgr ed to be <j gore"valuaBh^ The most importan 
of these was a newspaper produced by a 1930s version of desktop 
publishing. My printer was a homemade gelatinous block to 
which ink could be transferred from a glossy master sheet and 
thence to sheets of absorbent paper. The newspaper was impor- 
tant for me in many ways. Above all, it gave me a sense of identity. 
Adults asked one another, "What do you do?" and I could think 
of what I "did" as something more personal and distinctive than 
"going to school." 

Besides this, the newspaper made connections with several 
areas of intellectual and social development that would shape 
my high school years and beyond. I developed a sense of myself 
and a little skill as a chemist. My printing system was initially 
based on an article in Arthur Mee's Children's Encyclopedia but 
evolved over time and through many experimental variations. I 
developed a sense of myself as a writer, and I had to shoulder 
financial and managerial responsibilities that were no less real 
for being on a very small scale. And, perhaps most important in 
its subsequent impact on my life, the newspaper slowly drew 
me into the beginnings of political activism in the highly charged 
atmosphere of Johannesburg, where I lived from age seven 
through my mid-twenties. 

The particular facts of my story are unique to me as an individ- 
ual; the general principles it illustrates are not. Reading biogra- 
phies and interrogating friends has convinced me that all success- 
ful learners find ways to take charge of their early lives sufficiently 

24 • The Children's Machine 

is Jean Paget. The case has a mild irony in that this man <o ,avl, 

tot "cLn rifi a T ,PnatC StagCS ° f devek ». published 

ge"u In f ct Z h V16W " reVerendy 35 an ear * si 8" of Ins 
genius. In fact the short paper, which reports a sighting of a rare 

mat would be surprising in an average child of eleven I am 
mchned to think of the publication as being as much cau e a^ 
^ con e of piage(>s exceptiona] l^*™^ 

~ is L°^r at he woujd h - e — a ^ 

wanted to b' T ? ^ * * " a ^ imemional act - He 
town and writ 1 * ^ * his sma « ^wiss 

LTe b£l , PUbhShed thG artide to make ^e librarian 
take h lm senously enough to give him permission to do so What 

hELf . 3 ^ bUt that ^ same b °y of eleven took 

himself to Cm Tpiag^Tw " * ^ **" Preparing 
own develonL f ^l" 6 was Pacing taking charge of his 

onT e te and mr UPy ^ W °"< dfcHKd ^ *>""- 
one else and lhat, moreover, has no intrinsic valne—.,^™, 

find this offensive) ln part , femember ^ ^ 

Personal Thinking . 25 

objected as a child to being placed in that situation, but mainly 
because I am convinced that the best learning takes place when 
the learner takes charge, as the young Piaget did. Thus my an- 
tennae are always out for initiatives that will allow the purpose 
of School as a place for learning to coexist with a culture of 
personal responsibility. 

This must not be confused with the faddish idea that what 
children learn should be made "relevant"- so, teacher, don't 
just make them add numbers, pretend you are shopping in the 
supermarket. Chil dren are not easily dupe d. If they sense that 
they are being made to play a silly game, they will be dis- 
couraged from taking themselves seriously. I liked a little better 
what I saw at the Lamplighter School in Dallas, where the 
fourth-grade children actually had real responsibility for operat- 
ing an egg business. They bought the feed, cleaned the coops, 
collected and sold the eggs, and kept the profit, if there was any, 
at the end of the year. If they ended up with a loss, they had to 
explain themselves to the next class. But even this allowed very 
little opportunity for real initiative and only a minor sense of 
doing something really important. 

A deeper sense of doing something important in itself is visible 
in the project "Kidnet," developed in a collaboration between the 
National Geographic Society and Robert Tinker, who is responsi- 
ble for developing some of the best uses of computers for learning 
science. This project engages middle school students to collect 
data about acid rain. The individual schools send their data across 
electronic networks to a central computer where it is integrated 
and sent back to the local sites, where it can be analyzed and 
discussed in the context of globally important problems. The 
project hints at a vision of millions of children all over the world 
engaged in work that makes a real contribution to the scientific 
study of a socially urgent problem. In principle, a million children 
could collect more data about the environment than any socially 
affordable number of professional scientists. 

This is infinitely better than School's ritualistic worksheets and 

26 • The Children's Machine 

demonstration experiments, if only because the students feel they 
are engaged in a meaningful and socially important activity they 
really care about. However, what I like most is the opportunity it 
offers the students to break out of its own framework to engage 
in more self-directed activities. One way that students break out 
quite frequently is to use the expertise acquired in the project to 
engage in local environmental campaigns. Another example that 
pleased me particularly was expressed by a student who had 
worked out a plan to bypass the use of children to collect data by 
automating these operations. He explained that the children could 
then devote themselves to more important environmental work! 
This student could not actually implement this plan with the 
means provided by his school, but he was close: In a few years 
such projects will use hardware and software flexible enough for 
this student's plan to be widely implemented. 

A different example of computers giving children the opportu- 
mty to develop a sense of doing serious work is that of two 
fifth-grade boys with very different interests, one in science and 
the other in dance and music, who came together to create a 
"screen choreography" by programming a computer set up in the 
back of the classroom. What they were doing may not have been 
relevant, but it certainly felt vitally important to these boys and was 
seen as such by their teacher, who encouraged them to take time 
from regular class work for their project. Watching them, I was 
reminded of the newspaper I worked on as a child. I guessed that 
they were growing as independent intellectual agents, and anyone 
could see that they were learning what was for their age an 
unusual amount of mathematics and computer programming. 

This discussion, which intermingles learning incidents from my 
life and Piaget's with incidents from the lives of children in con- 
temporary schools, represents an alternative to the methodology 
favored by the dominant "scientific" school of thought. Research- 
ers, following the so-called scientific method of using controlled 
experiments, solemnly expose children to a "treatment" of some 
sort and then look for measurable results. But this flies in the face 
of all common knowledge of how human beings develop Al- 

Personal Thinking • 27 

though it is ob vious ro me that m y newspaper played_ £profounri 
rojg j" m v intell ectu al de v elo pment T i m pretty snrp t lianio test 
would have detected its role by comparing my "performance " the 
' day before I started a ndjJiLmjriQiilhsJater. The significant effects 
emerged over a much longer period, to be measured, probably, in 
years. Moreover, an experiment that gave a hundred children "the 
experience of producing a newspaper," even if continued for 
several years, still would miss the point of what happened to me. 
T he significant engagement was toopersonal to be expected to 
operate as a mass effect; I fell in l oye with my newspapering (as 
I did wit h mathematics arid" other-ar eas of knowled ge) for reasons" 
that are as personal and in a sense as unreproducible as those that 
determine any kind of falling in love. 

The method of controlled experimentation that evaluates an 
idea by implementing it, taking care to keep everything else the 
same, and measuring the result, may be an appropriate way to 
evaluate the effects of a small modification. However, it can tell 
us nothing about ideas that might lead to deep change. One 
cannot simply implement such ideas to see whether they lead to 
deep change: A megachanged system can come into being only 
through a slow, organic evolution, and through a close harmony/ 
with social evolution. It will be steered less by the outcome 
of tests and measurements than by its participants' intuitive 

The most powerful resource for this process is exactly what is 
denied by objective psychology and the would-be science of ed- 
ucation. Every one of us has built up a stock of intuitive, em- 
pathic, commonsense knowledge about learning. This knowl- 
edge comes into play when one recognizes something good 
about a learning experience without knowing the outcome. It 
seems obvious to me that every good teacher uses this kind of 
knowledge far more than test scores or other objective measure- 
ments in daily decisions about students. Perhaps the most im- 
portant problem in education research is how to mobilize and 
strengthen such knowledge. 

One step toward strengthening it is to recognize it. The denial 

28 • The Children's Machine 

of persona] intuitive knowledge has led to a profound split in 
thinking about learning; the split recalls the theory that each of us 
has two brains which think in fundamentally different ways. By 
analogy, one might say that when it comes to thinking about 
learning, nearly all of us have a School side of the brain, which 
thinks that School is the only natural way to learn, and a personal 
side that knows perfecdy well it is not. 

A second strategy for strengthening the personal side and 
breaking the stranglehold of the School side is to develop a meth- 
odology for reflection about cases of successful learning and espe- 
cially about one's own best learning experiences. Analogies with 
two events in the. history of aviation — a case of true mega- 
change — will clarify my thinking. 

People who dreamed about making flying machines looked at 
birds in the same spirit as I want to look at examples of successful 
learning. But it was not enough simply to look and copy. Many 
were misled into thinking that the essence of bird flight was the 
flapping of wings. Even the great Leonardo was drawn into the 
vision of an ornithopter, a machine that would look like a bird and 
fly by flapping birdlike wings. This was not the way to make a 
flying machine. Nevertheless, it was the observation of birds that 
provided the secret. My analogy here concerns John Wilkins, a 
seventeenth-century bishop, scientist, and founder of the Royal 
Society. Wilkins could not have been the first to observe that birds 
could fly without flapping their wings. But he was one of the first 
to see the importance in this otherwise banal observation. He was 
right. The simplicity of a gull soaring without a visible movement 
of its body became the model that eventually led to formulating 
the principle of lift, the concept underlying both the understand- 
ing of natural flyers and the making of artificial flyers. We have to 
learn to see successful learning through the prism of such power- 
ful ideas. 

The second event happened as an indirect result of the first. 
The year 1903— when a powered airplane first flew success- 
fully—was a turning point in the history of transportation. But the 

Personal Thinking • 29 

famous flyer made by Wilbur and Orville Wright did not prove 
itself by its performance. The duration of the best of several flights 
that day was only fifty-nine seconds! As a practical alternative to 
the horse-drawn wagon, it was laughable. Yet imaginative minds 
could see in it the birth of the industry that would lead to the 
jumbo jet and the space shuttle. Thinking about the future of 
education demands a similar labor of the imagination. The preva- 
lent literal-minded, "what you see is what you get" approach 
measuring the effectiveness of computers in learning by the 
achievements in present-day classrooms makes it certain that to- 
morrow will always be the prisoner of yesterday. Indeed, the 
situation in education is often even worse than judging the effec- 
tiveness of airplanes by the fifty-nine-second flight. It is more like 
attaching a jet engine to an old-fashioned wagon to see whether 
it will help the horses. Most probably it would frighten the animals 
and shake the wagon to pieces, "proving" that jet technology is 
actually harmful to the enhancement of transportation. 

I have in my files a large collection of scientific papers reporting 
experiments that try to measure "the effect of computers on learn- 
ing." It is like measuring the flight characteristics of the Wrights' 
flyer to determine "the effect of flying on transportation." The 
significance of the flyer could be appreciated by hard imaginative 
work based on understanding the principles, such as "lift," which 
lay behind the design. In order to find the corresponding princi- 
ples for learning, we have to look into ourselves as much as at 
computers: Principles such as "taking charge" and "intellectual 
identity" and "falling in love" (as I used in talking about my 
newspaper) have come to play that role in my own thinking as a 
direct result of observing myself when I seemed to be flying 
intellectually. The incidents in the rest of this chapter highlight 
some others. 

As I grew up, learning became a jiobbv. Of course any hobby 
involves learning, but most people are more interested in what 
they learn than in how the learning happens. In fact, most learn 

30 • The Children's Machine 

without giving a thought to learning. I often go to the other 
extreme. I learned to juggle, to fly a plane, and to cook, not only 
because I wanted to do these things but also because I wondered 
what the learning would be like. Though I came to love all these 
hobbies for their own sake, part of my pleasure in them has 
always been that of observing myself learn and making up theo- 
ries about how I do so. A good example of this process is how I 
learned to make croissants. 

When I got croissant making right after many, many failures, I 
allowed myself some elation but then began to worry about what 
had happened. One day I couldn't do it, the next day I could! 
What had changed? In order to reconstruct the moment of transi- 
tion, I tried to recapture the state of "inability" I had been in the 
day before. At first I thought in terms of external factors such as 
the proportions of ingredients, the times of rising and resting, and 
the temperatures of dough, working surface, and oven. But vary- 
ing these did not seem to account for my prior uneven results. 

When I eventually did relive the key moment, I had learned 
about much more than making croissants. The difference between 
before and after lay in feeling the degree of "squishiness" of the 
butter through the squishiness of the pastry dough and through 
my heavy marble rolling pin. Trying to capture this deliberately 
seemed at first like the princess and the pea. I tried many times. 
It was only when I decided that I had enough and would give up 
for the day that a breakthrough happened. On my marble slab was 
a last parcel of butter wrapped in dough. Wondering what to do 
with it, I playfully flattened it with the rolling pin, relaxed, without 
trying to do anything in particular— and all of a sudden I felt 
distinctly the structure of the mass of matter. Once I felt it, I knew 
"in my fingers" how to make a croissant, and now when I try after 
an interval of several years, the knack always comes back by the 
second batch— though if I had to do it on a school test I would 
fail, because 1 need the spoiled first try to get the feel for the 
successful second one. 

When I retell such experiences to an audience of educators, I 

Personal Thinking - 31 

always hope that someone will be annoyed by my talk of crois- 
sants and say: "What has this to do with grammar or math or 
writing business letters? Naturally in cooking you have to learn to 
feel the relationship of your body to matter. But math is not about 
feeling relationships of your body to numbers." I like this reaction 
because it brings out into the open something that lurks in the 
culture and allows me to confront it. 

A few years ago I would have begun with the rejoinder: "You 
think that math does not have anything to do with the body 
because you are not a mathematician; if you were you would 
know that mathematics is full of gut feelings and all sorts of 
kinesthetics." Today I would say it the other way around: "The 
reason you are not a mathematician might well be that you think 
that math has nothing to do with the body; you have kept your 
body out of it because it is supposed to be abstract, or perhaps a 
teacher scolded you for using your fingers to add numbers!" This 
idea is not just metaphysics. It has inspired me to use the com- ' 
puter as a medium to allow children to put their bodies back into 
their mathematics. 

My favorite example is an invention called "the turtle." You 
can think of this as a drawing instrument whose simplest use 
will become clear from the following scenario. Imagine that you 
are looking at a computer screen. On it you see a small turtle, 
which moves when you type commands in a language called 
"turtle talk," leaving a line as it goes. The command "Forward 
50" causes the turtle to move straight ahead a certain distance. 
"Forward 100" will make it move in the same direction twice as 
far. You soon get the idea that the numbers represent the dis- 
tance it moves; they can be thought of as turtle steps. Now if 
you want to make it go in a different direction, you give it a 
command like "Right 90." It stays in the same place but turns on 
itself, facing east if it had previously been facing north. With this 
knowledge you should easily be able to make it draw a square. 
If that's easy for you, you can think about how to draw a circle, 
and if that's easy, you can try a spiral. Somewhere you will meet 

32 • The Children's Machine 

your level of difficulty, and when you do I'll give you this piece 
of advice: Put yourself in the place of the turtle. Imagine yourself 
moving in a square or a circle or a spiral or whatever it may be. 
You may resist for a while because you are tense and trying too 
hard, as I was with my croissants. But when you let yourself go, 
you will find that there is a richer source of mathematical knowl- 
edge in your body than in classroom textbooks. 

Learning to speak French was one of my most instructive learn- 
ing experiences. Although this was not a case of learning for its 
own sake — I went to live in Paris to complete my doctoral re- 
search in mathematics — my professional purpose was interlaced 
with playful learning experiments. For example, I developed a 
relationship with an eight-year-old boy who was delighted to be 
my "professor." He was young enough to be "studying French" at 
the same time as I was. Although he was a native speaker, he was 
learning spelling and grammar at school and was acquiring vocab- 
ulary at an appreciable rate. I was able to compare the speed and 
pattern of my progress with his, and in doing so established a 
curious fact: By any measure I could think of, I was learning faster. 
I could have attributed the discrepancy between this observation 
and the common linguistic sluggishness of adults to some kind of 
special "gift for languages." I didn't. I explain the discrepancy by 
the fact that I was learning French mosdy like a child but could 
also take advantage of some sophisticated ideas that a child would 
not know. On the one hand, I was open to playful immersion; on 
the other, I could make occasional use of formal linguistics. Some- 
where between the two was the fact that my learning of French 
seemed to be facilitated by experimenting (or playing) not only 
with French but also with learning itself. Studying one's own 
learning process — as the example of croissant making also 
shows — can be a powerful method of enhancing learning. In any 
case, looking back I see an important root of my present ideas in 
this recognition of the adva ntages of com bining childlike and 

a ^Hi!llK£J^5_Cif4earning. ' " " 

Although my mathematical research in Paris earned me my 

Personal Thinking • 33 

Ph.D., the Parisian discovery that had the biggest impact on my 
life was Jean Piaget, who at the time was giving a course at the 
Sorbonne. I got to know him and was invited to work in his center 
in Geneva, where I spent the next four years and became passion- 
ately interested in children's thinking. If the key ideas in this book 
first crossed my mind then, however, they were in the most nebu- 
lous guise. In particular, I made no connection that I can remem- 
ber between my own learning and the process of intellectual 
development of children on which we worked at Piaget's center. 
The reason is significant: We were all too serious and too formal 
about children's thinking. Of course we thought about their play; 
it was Piaget who coined the oft-quoted line thatj jlay is child's 
.work. But no one in that environment was looking at the other 
half of this pithy aphorism: the idea that work (at least serious 
intellectual work) might be adult's play. We thought of children as N 
"littjescientists'' but did not think much about the co mplementa ry 
idea ofyiewing scient ists as "bjgchikiren.'' 

Following the four years in Geneva, I became a professor of 
mathematics ,a^Mn\^lany factors made the move attractive. There 
was the prospect of access to computers and of working with 
Marvin Minsky and Warren McCulloch, as well as a wonderful 
s gpsg of p l ayfulness that I had experienced there on brief visits. 
When 1 finally arrivedTall this came together in all-night sessions 
around a PDP-1 computer that had been given to Minsk v. It was 
pure play . We were finding out what could be done with a com- 
puter, and anything interesting was worthwhile. Nobody yet 
knew enough to decree that some things were more serious than 
others. We were like infants discovering the world. 

It was in this situation that I thought about computers and 
children. \_ was playing like a child and experiencing a volcanic 
explosion of creativity. Why couldn't the computer give a child the 
same kind of experience? Why couldn't a child play like me? What 
would have to be done to make this possible? 

These questions launched me on a new quest guided by the 
Robin Hood-like idea of stealing technology from the lords of the 

34 • The Children's Machine 

laboratories and giving it to the children of the world. A first step 
in the quest was to recognize that one of the sources of the 

arourjdthejde a i of program ming. The situation is quite analogous 
to the way priests of other ages kept power from people by 
monopolizing the ability to read and write, and by keeping what 
they considered the most powerful knowledge in languages the 
common people could not understand. I saw the need to make 
computer languages that could be "vulgarized' '-made available 
to ordinary people and especially children. 

This has turned out to be a long and difficult task. Computer 
languages, like natural languages, cannot be "made"; they have to 
evolve. What could be made was a first shot at such a language 
named Logo, which would serve as a starting point for a longer 
evolution that is in fact still continuing. 

For the sake of concreteness, the ideas in this book are devel- 
oped through the story of my own inventions. I make no secret of 
the fact that I love and value some of them. I believe that some 
may even have a long-term future. But I repeat that my purpose 
here is not to tell the reader how to do things right but to provoke 
and fuel imaginations. In this book my real-life inventions serve 
the same purpose as the imaginary examples of time travelers and 
hypothetical nineteenth-century engineers. They are meant to 
evoke further ideas, to prepare our minds for other, much more 
exciting inventions still to be made. My purpose could not be 
further removed from advocating a particular invention as the 
solution to the problem of education, rather, each example is 
meant to serve as a pointer to a vast area of new opportunities for 
educauonal invention. My goal in relation to Schoolers-or to 
anyone who thinks that any form of learning is the right and 
natural form of learning-is to stir the imagination to invent 
alternates. Piaget said that to understand is to invent He was 
thinking of children. But the principle applies to all of us 

School: Change and 
Resistance to Change 

I made a first pass at creating images of educational mega- 
change in Mindstorms: Children, Computers, and Powerful 
Ideas, written in the late 1970s, a time when personal comput- 
ers were still novelties. IBM had not yet moved into the field, nor 
had the Japanese. The original Apple was mostly the darling of, 
enthusiastic computer hobbyists. 

The subtitle of the book reflects a gap in my experience and 
knowledge by mentioning children and excluding school. Chil- 
dren's involvement with computers had already begun. The first 
primitive video games had appeared, and one could mount ex- 
periments in which large and expensive machines simulated the 
still nonexistent personal computer. Children's interest in what 
they could do with the machines was not distracted by knowing 
that a million-dollar machine stood behind the terminal used in 
the experimental setting. No similar experiment could be done 
on what schools might do in a world in which computers would 
be everyday objects. Their reaction was so profoundly deter- 
mined by considerations of price and size that no "simulation" 
could provide insights into how they would allocate real budget 
and accept real changes in their organization. It is not surprising, 

36 • The Children's Machine 

then, that my discussion of schools lacked the texture that real 
experience gave to the discussion of how computers could me- 
diate between children and ideas. I was not the only one to 
suffer from this failing; in fact, a persistent tunnel vision contin- 
ues to deform public discussion of the relationship between 
technology and schools. My purpose in this chapter is to de- 
velop a wider-angled view. 

Mindstorms was written at a turning point in the development 
of educational computing. At that time, there were at most a 
handful of classrooms in which anything like the classroom inci- 
dents mentioned in the previous chapter could possibly have 
taken place; in fact, the only activities in the field that I know of 
were two formal research projects, my own and a related one 
mounted by Alan Kay, a seminal contributor to the idea that the 
computer could be an instrument for everyone. Yet two years after 
the book was published, there were hundreds of classrooms in 
which one could see similar events, and two years later still, there 
were tens of thousands. This growth of a school computer culture 
was still far from megachange, but it had reached proportions that 
made it incomparably richer as a source of insight into educational 
change than the cramped experiments of the previous decade. In 
ten years American schools had bought three million computers; 
tens of thousands of teachers enrolled in classes to learn about 
computers; new industrial giants moved into the education mar- 
ket; twenty thousand items purporting to be "educational soft- 
ware" were offered for sale. 

These dramatic events did not fail to attract media attention. 
Apart from the sheer numbers, the very idea of a small child using 
a computer gave people a sense that something new, exciting, and 
a little disturbing was in the air. Add to this the photogenic quality 
of children with eyes made brighter by the light of the screen, and 
it is understandable that computers in schools for a while aroused 
more enthusiastic coverage in the press than sensible discussion 
about what it all meant. But what did it mean? What sensible 
questions would lead to understanding what was happening and 

School: Change and Resistance to Change • 37 

where it might go? A headline in the Wall Street Journal reflected 
the doubts of sensible people interested in the bottom line. 

ROOMS are small. The tone of skepticism is understandable. Talk of 
crisis in the schools was on the rise. Even in the uncritical climate 
of Reagan's Washington, the report "A Nation at Risk" had dramat- 
ically proclaimed this. It is not surprising that questions were 
asked: Where are all those computers we have heard so much 
about? What are they doing? Far from producing improvement, 
they seemed unable even to stop the deterioration. 

I offer two replies to the kind of doubts raised by the Journal, 
one relatively superficial and one more serious. The superficial 
response concerns the use of the word many to describe the 
number of computers in the schools, which at the time was be- 
tween one and two million. Was this a lot? Yes, if one thought of 
a mountain of computers piled up in one's backyard. No, if one 
divided it by the number of students in all those classrooms. I 
know what it is like to have had my intellectual life change, and 
more than once, through using computers. In addition to intellec- 
tually deeper changes, my writing habits have changed because I 
take a computer on a plane, in a car, out on the lawn, or to the 
bathroom; and my communication habits have changed as a con- 
sequence of so many colleagues and friends being in touch 
through electronic mail. Just two days ago I clarified my thinking 
about the economic reform in Russia by programming a soft simu- 
lation of economic competition. This can happen because I have 
a computer, in fact several computers, within reach at most times. 

The critical level at which computers really make a difference is 
surely less than what I have, but equally surely more than what 
schools offer most students. A million computers divided among 
fifty million students gives each of them one-fiftieth of a computer. 
I do not think that the significant benefits that computers have 
brought me would have accrued from a fiftieth of a machine. 
Simple arithmetic, which is not altered in principle by the fact 
that some schools may have had three or four times the average 

38 • The Children's Machine 

number of computers, provides so obvious an explanation of the 

wrTthe T, ,e ^ W ° nderS Wh6ther the ™ » who 
wr e the arude were really thinking in any concrete sense about 

what they were writing. I wonder whether they would be sur 

pnsed if observation of schools in some country where only one 

ISSZZ? T d be provided for ™ - d ~ 8 

gested that wntmg does not significantly help learning 

pro^ceTT 3 I™" nUmber ° f C ° m P Uters is u ^ely to 
produce b,g change might seem to be contradicted by some of the 

modems mentioned earlier, where children enjoyed the expen 

ence of sharing two computers with a whole class. There T no 

doubt that, with or without computers, an isolated even 2 

of^jr iP ^ e imP ° rtant ime,leCtUal ^ Bu < — 
often change requ,res a much longer and more social computer 

classroom. In chapter 6 well meet Debbie, who did have an "aha" 

X7 n w C h e ic1 T ° f bu, she was ifa 

school which owned over a hundred computers Also such 

SEe^S rCVerSib,e ' " ^ ^ - ° f ~ w^ 
experience with computers gave him his first taste of enjoyable 

and successful learning at school. This student who had been 

as omshed his teachers, his parents, and even himself. However 
*. tas e o something better aggravated his dislike of the ways 
of regular classroom life to such an extent that in the end hlre- 

Zr^T even more deep,y *■* he had bef - * ~ 

ih-TcTnuZ^ SmaU effeCt inV ° ,VeS dee P er P robIe - than 
that of numbers. In the early 1980s there were few microcomnut 

« - schools but those few were almost all in the clasTrooms of 

--nary teachers, most of whom employed them in a "" g e l 

lum Z ' mmng 3CrOSS Sch ° 0, ' S practices ^ balkani.ed curi- 
um and impersonal rote learning. Thereafter, however the Dat 

C^r Iy - The r lative and * e power in 

computers were movmg from teachers to school administra- 

School.- Change and Resistance to Change • 39 

tions— most often at the city or even at the state level. When there 
were few computers in the school, the administration was content 
to leave them in the classrooms of teachers who showed greatest 
enthusiasm, and these were generally teachers who were excited 
about the computer as an instrument of change. But as the num- 
bers grew and computers became something of a status symbol, 
the administration moved in. From an administrator's point of 
view, it made more sense to put the computers together in one 
room— misleadingly named "computer lab"— under the control 
of a specialized computer teacher. Now all the children could 
come together and study computers for an hour a week. By an 
inexorable logic the next step was to introduce a curriculum for 
the computer. Thus, little by little the subversive features of the 
computer were eroded away: Instead of cutting across and so 
challenging the very idea of subject boundaries, the computer 
now defined a new subject; instead of changing the emphasis 
from impersonal curriculum to excited live exploration by stu- 
dents, the computer was now used to reinforce School's ways. 
What had started as a subversive instrument of change was 
neutralized by the system and converted into an instrument of 

This analysis directly contradicts the answer most commonly 
given by researchers when asked why computers have made so 
little dent in the problems faced by School. They are inclined to 
say that "schools don't know how to use the computer"; and they 
propose to remedy this by more research on methods of using 
computers, by developing more software, especially software that 
will be easier to use, and by setting up channels of dissemination 
of knowledge about computers. They are fundamentally wrong. 
Of course, research will increase the variety and effectiveness of 
uses of computers, but this is not what will change the nature of 
computer use in schools. The shift from a radically subversive 
instrument in the classroom to a blunted conservative instrument 
in the computer lab came neither from a lack of knowledge nor 
from a lack of software. I explain it by an innate intelligence of 

40 • The Children's Machine 

School, which acted like any living organism in defending itself 
agamst a foreign body. It put into motion an immune reacSn 

Progressive teachers knew very well how to use the computer 
their own ends as an instrument of change; SchooTLTv^l 

out o I? SU K VerSl0n ta ±e bUd N ° °" e in *e story a «ed 
out of ignorance about computers, although they miaht hZ Z 

This view of the development of computers in schools points 
~ce or m aPPr ° aCh t0 ^ Ca " be 'earnedtm 
JSS article " r h00lS th3n ^ ° f the W «» *™ 

« t T Shifted from " Did » succeed, yes 
or no. to What actually took place below the surface- what can 
we learn from the experience that will inform future s trltels " 

tealhfnf ll ana H° 80US "° ° f developmental 

teachmg, whtch eschews molding a mind as if it were a passive 
medium and instead tries to collaborate with the student's TvJ 
opmental patterns. If the student does not 
Pected way, the developmental teacher trie SS^* 

below the surface one can often see an inner coherence in what 
appeared to be just plain wrong, one sees mental Si ^ 
stand m the way of progress, and one sees dynamic elements h! 
can be mobilized to serve it. Midterms' 
were quite thoroughly developmental, but I now blush at r^ 

ather m guiding educational innovation. School will n « co^Z 

S'c/zoo/. Change and Resistance to Change • 41 

It will come to use them well (if it ever does) as an integral part 
of a coherent developmental process. Like good developmental 
teachers, researchers can contribute best if they understand 
change in School as development, and support this by transferring 
the ideas that were successful for understanding change in 

Piaget vastly increased understanding of children by means of 
an idea that seems, as many of the greatest ideas do, ridiculously 
obvious once one has understood it. All mental operation, he said, 
has two facets, which he calls assimilation (changing your repre- 
sentation of the world to fit your ways of thinking) and accommo- 
dation (adapting your ways of thinking to fit the world). School's 
first response to the computer was, quite naturally, one of assimi- 
lation. School did not let itself change under the influence of the 
new device; it saw the computer through the mental lens of its 
own ways of thinking and doing. It is a characteristic of conserva- 
tive systems that accommodation will come only when the oppor- 
tunities of assimilation have been exhausted. In the interim one 
sees interesting subplots of the developmental story as the system 
displays its ability to block off incipient accommodations. 

In education the acronym CAI (Computer Aided Instruction) is 
used for the fully assimilated usage of computer technology. CAI 
refers to programming the computer to administer the kinds of 
exercise traditionally given by a teacher at a blackboard a text- 
book, or a worksheet. This is so far from challenging the assump- 
tions of traditional School that critics frequendy ask whether it 
does anything at all to justify the cost of computers. The most 
hardened skeptics describe the computer as "a thousand-dollar 
flash card," and what it does as "drill and kill." 

Advocates reply by listing advantages of having a computer ask 
a student, for example, to calculate 35 percent of $2.00 Those 
most frequently cited include immediate feedback (one will learn 
more from a mistake by being told immediately not only that one 
is wrong but why); individualized instruction (the questions 
can be matched to the level of competence of the student)- and 

42 • The Children's Machine 

neutrality (the computer is not subject to biased perceptions, by- 
student of teacher and vice versa, related to race, gender, or 
personal history). Statistical studies show that the introduction of 
CAI will often modestly raise test scores, especially at the low end 
of the scale. But it does this without questioning the structure or 
the educational goals of traditional School. 

The first sign of incipient accommodation came, as perhaps it 
always does, through another assimilation. Large numbers of pro- 
gressive teachers were able to assimilate the computer to their 
ideas about teaching (and about getting around School), and this 
gave rise to a movement that I shall call the Progressive Educa- 
tional Technology (or PET) Movement. 

CAI is older than PET — in fact, it dates back almost as far as the 
idea of the computer. When I first entered the computer scene it 
was already in existence and, in fact, held a monopoly on thinking 
about computers in education. The first formulations of ideas that 
would become those of PET emerged slowly from the develop- 
ment of Logo and the turtle, mentioned in the last chapter. In the 
early 1970s this stream of development was joined by another 
under the leadership of Alan Kay, a computer scientist, musician, 
and inspiring personality who was, I believe, the first person to 
use the words personal computer. At the end of the 1970s, these 
ideas filtered slowly into the awareness of progressive teachers 
who happened also to be in touch with the excitement that ac- 
companied the first microcomputers. 

In 1980 three events came together to give a powerful boost to 
the awareness among teachers that computers could be used in 
the spirit of progressive education. Mindstorms set this out in 
easily accessible form, inexpensive personal computers reached a 
level of performance that could support a usable version of Logo, 
and Logo software became commercially available. The result was 
a grass-roots movement that generated many thousands of class- 
room implementations of PET. The character of this movement 
and the depth of its conflict with School's philosophy cannot be 
captured by abstract formulas. Instead, some anecdotes will con- 
vey the texture of the conflict. 

School: Change and Resistance to Change • 43 

Even now I can close my eyes and see a 1981 scene in a fifth-grade 
classroom in a New York City public school. Two worlds seemed 
to coexist in one room: At one end, a teacher, Thelma, was giving 
a "lesson" at the blackboard; at the other, a cluster of students was 
working with two computers. The computer group ran into a 
problem and sent someone to "ask the teacher." Thelma said, 
"Maybe Bill can help" — and continued her lesson without miss- 
ing a beat, quite unperturbed by the fact that Bill had now joined 
the ranks of students who weren't even pretending to listen to her. 

The front and the back of the room were separated by much 
more than a difference between the technology of the computer 
and the technology of the blackboard. A far greater difference 
marked the children's relationship with what they were doing. In 
front, they were following someone else's agenda; in the back, 
they were following their own. Among them, the ones I remember 
most vividly were Brian and Henry. 

When I came into the room I was captured, as was every visitor, 
by the spectacular visual effects on the computer screen produced 
by programs written by the two students. Colored shapes moving 
in complex intertwining paths spoke immediately to a choreo- 
graphic talent, a sense of movement and drama. I had to examine 
the display more closely before I was able to recognize the mathe- 
matical sophistication that went into controlling the geometry and 
dynamics of the movements. These boys were engaged in a math- 
ematical exercise fundamentally different from calculating 35 per- 
cent of $2.00 on command. Their activity included such calcula- 
tions (together with more sophisticated mathematical thinking) 
but not as set exercises; the calculations came up in the course of 
doing a larger and personally motivated project. In fact, I chose 
the percentage problem as my example to illustrate CAI expressly 
because it is quite like one of the many different kinds of calcula- 
tional problem Brian and Henry did have to solve: For example, 
at what speeds do two objects have to move so as to arrive at the 
same place at the same time if one follows a path whose length is 
35 percent of the length of the other? 

This latter problem is harder than the usual School kind 

44 • The Children's Machine 

because its geometric form makes it more complex and because 
the boys would have to scrounge and scurry to find out how to 
do it; ask a teacher or fellow student, look in a book, work by 
analogy with another situation, try to invent a method, resort to 
trial and error. Children never seem to mind: What makes School 
math repugnant for the Brians and boring for the Henrys is not 
that it is "hard" but that it is a senseless ritual dictated by the 
agenda of a set curriculum that says, "Today, because it is the 
fifteenth Monday of your fifth-grade year, you have to do this sum 
irrespective of who you are or what you really want to do; do what 
you are told and do it the way you are told to do it." The point is 
not that their teacher was willing, as some advocates of "free 
school" have proposed, to let her charges do anything they 
wanted. Far from it: She imposed very high standards and de- 
manded commitment and discipline. But when Brian and Henry 
wanted to do something that was deeper, more instructive, and 
more intellectually demanding than the fifth-grade curriculum, her 
instinct as a teacher told her to encourage them. 

The previous relationship between these boys says a great deal 
about School as an intellectual environment. Although these two 
boys had been classmates for four years, they hadn't talked to one 
another much until the computers brought them together. They 
had already developed strong individual interests in life, and al- 
though School threw them into the same room, it provided few 
opportunities for these interests to meld into real relationship. 
Thus School squanders its most valuable resource— the inter- 
change between the most intellectually interesting students. 

Henry had always been the math whiz and his fantasies were 
in science fiction; Brian had always cared about music and 
dance. Watching him, one had no doubt that the sensory and 
bodily aspects of the world were important to him. Henry was 
awkward in his movements, one might say out of touch with his 
body. He cared little about clothes and colors. But although this 
cut him off from a significant area of experience, up to the ar- 

School: Change and Resistance to Change • 45 

rival of the computers he had not experienced it as a defi- 
ciency— cenainly not as a deficiency relevant to his schoolwork. 
Science and mathematics, the areas he enjoyed and excelled in 
most, seemed to have no relationship with sensory enjoyment 
and physical action. Indeed, this perception surely contributed 
to his attachment to these activities, just as it contributed to 
Henry's indifferent response to them. 

When their teacher brought computers to the classroom, there- 
fore, the two students had very different expectations. Henry 
knew instantly that this was going to be his thing; without any 
doubt he would be "best at computer." Brian's reaction mixed a 
mild curiosity with a twinge of apprehension. 

Henry found that the route to making the most of the com- 
puter went through establishing a working relationship with the 
least likely person in the class, Brian the dancer. Brian found for 
the first time that mathematics could be a personally exciting 
medium of self-expression and the basis of a genuinely interest- 
ing friendship. 

The story needs some background information about how the 
computers were introduced into the classroom. Thelma had at- 
tended a summer workshop sponsored by the National Science 
Foundation on using computers in schools. She had enrolled with 
little idea of what she would do there, and with some trepidation, 
for she had never thought of herself as a "technology person." But 
computers were in the air. She had friends who spoke about the 
microcomputer revolution, about how these new machines 
would give ordinary citizens access to information previously 
monopolized by big corporations and government agencies. She 
had read that they would lead to new methods of teaching. But, 
most important, she understood that children loved them, and the 
fame spirit that led her to bring hamsters and plants and posters 
f*nd all manner of what she called "junk" into her classroom 
^Parked her interest when she heard about the summer course. 

Thelma's first contact with computer programming consisted of 
Usin 8 Logo to instruct the computer to draw patterns of lines on 

46 • The Children's Machine 

its screen. She was actually surprised at her surprise at finding that 
she could make the computer draw something she wanted; even 
getting it to draw a simple square gave her a sense of pleasure at 
beginning to "own" a technology so symbolic of what was most 
modern and most powerful. After a few days her ability to pro- 
duce more intricate patterns and set objects in motion on the 
screen evoked associations with computer art and with the special 
effects in movies like Star Wars. 

By bringing this kind of programming technique back to her 
classroom, Thelma inspired the collaboration between Brian and 
Henry. In her class, creating animation on the screen became the 
most common choice made by children who were free to do what 
they wished with the computers. 

Some children created realistic animations to tell a story. Not 
surprisingly, Henry was among those who preferred more stylized 
forms whose visual interest was in the complexity of shapes and 
patterns of motion rather than a narrative content. Henry quickly 
understood the technical side of programming. Earlier than any- 
one else in the class, he knew exactly how to create figures on the 
screen and make them move. He had enough visual imagination 
to try for effects whose nature is evoked by the names he gave 
them: "Fireworks" or "Star Wars" or "The Big Bang." His talent for 
mathematics paid off in his easy mastery of techniques for pro- 
gramming an object on the screen to begin moving almost imper- 
ceptibly and then gradually accelerate. Something more creative 
showed itself in what a mathematician would call "generalizing 
the idea," when he realized that the same techniques could be 
used to make a sound mount in pitch from a low growl to a high 
scream and eventually disappear into the ultrasonic range. From 
a School point of view he was doing very well indeed, but some- 
thing was missing. 

Henry took pleasure in the mathematical cleverness behind his 
displays but was disappointed by the total effect. His problem was 
not simply that fellow students drew more "oohs" and "aahs" 
when they showed their work. He could feel that his creations 

School: Change and Resistance to Change • 47 

lacked something he did not know how to achieve or even name, 
certain qualities that another fifth-grade student described as 
"grace" and "excitement." Perhaps for the first time in his life, he 
felt the pang of awareness of an intellectual limitation. His mind 
was ready for a breakthrough. 

The idea came to him when he saw Brian dancing in a school 
corridor. Recognizing that Brian's movements had just what his 
screen displays lacked, Henry was led quickly to the inspired 
thought that they might work together to produce the best screen 
choreography ever made! The thought led to a long-term working 
relationship. Together the two boys created something that nei- 
ther could even imagine alone, and in doing so learned much 
more than math test scores are capable of measuring. 

They certainly mastered a great deal of technical mathematics. 
Moving those objects on the screen required a description of the 
movements in mathematical language that went beyond even 
Henry's previous knowledge. They represented an object's speed 
as a variable, and then set up formulas to vary it. They learned to 
think of directions as angles measured in degrees. They picked up 
the idea of doing geometry by coordinates in a way much closer 
to the living and personal discovery through which Rene Des- 
cartes first came upon it than to the deadly formal presentation of 
math textbooks. But this kind of knowledge was only a small part 
of what they learned. 

Beyond developing technical mathematical skills, they came 
to experience mathematics in a very different way. It became 
something to be used purposefully; they felt it as a source of 
power in pursuing important and deeply personal projects. I am 
not sure that people who have not experienced mathematics in 
this way can fully appreciate how heady, how powerful, it can 
be. An analogy might be the experience of learning to ski. At 
first one is instructed in a series of awkward movements: Shift 
your weight, bend your knees, and so on. One obeys the com- 
mands but it feels as if one is clumsily acting at being someone 
else. Then one day comes a conversion experience. One is flying 

48 • The Children's Machine 

(or so it seems) down the slope. One's own knees are flexing 
and extending, one's own weight is shifting. One doesn't have 
to "do" these things; they flow as inseparable parts of a fluent 
and joyous movement. 

Certainly for Brian and possibly for Henry too, their collabora- 
tive work had elements of such a conversion experience. Mathe- 
matics became more like flying down the hill than like bending 
one's knees and shifting one's weight at the command of an 
instructor. This does not mean that doing mathematics became 
easy: Quite the contrary, just as in the experience of skiing, there 
was the frustration and never-ending struggle of mastering new 
techniques and handling new challenges. It became harder as they 
engaged with more serious problems, but when one is deeply 
involved in something, "easy" is not what one wants. If it were, 
one would spend the rest of one's skiing life going down the 
easiest slopes; but most people, especially young people, seek the 
challenge of moving on to more interesting terrain. 

The analogy with skiing brings out an experiential side of 
Brian's and Henry's mathematical learning that goes beyond ac- 
quiring technical knowledge. The analogy also suggests ways in 
which their learning went beyond mathematical learning even 
in the widest sense of mathematics. The use of the word fluent in 
reference to skiing reflects a relationship with activities where the 
word is more often applied, for example, language or musical 
performance. I want to generalize this notion to other activities 
and suggest that Henry and Brian, in rather different ways, were 
learning to be fluent in the use of mathematics. They were also 
learning the feel of fluency. I want to suggest that fluency in its 
own right is an important and insufficiently recognized area of 

Brian came to the collaboration with certain kinds of fluency. 
His fluency in dance, in body movement, was what drew 
Henry's attention and what provided the basis of the collabora- 
tion. But there was more to the pattern of where he was and 
was not fluent than simple competence in dance. Brian was a 

School: Change and Resistance to Change • 49 

fluent talker; he could tell a story in a way that would hold rapt 
attention. His talking had exactly those qualities of "grace" and 
"excitement" that were missing in Henry's programming. But an 
amazing thing happened when he took a pencil to write. What 
came out was totally lacking in these qualities. What he put on 
paper was one laboriously wooden sentence after another. The 
contrast of oral fluency with plodding writing is extremely com- 
mon and a major cause of illiteracy: Those who know from their 
oral skills what it is like to use language fluently are repelled by 
their own clumsiness when forced to write and often end up 
simply refusing to do it. 

For people like Brian, the opportunity to make animations 
provides a way to extend their domain of fluency into an area that 
shares essential qualities with speech, body movement, and writ- 
ten language. It may take time to get your screen creation right, 
but once you do you can move with it; you can feel its excitement 
in a very direct bodily way. On the other hand, the program is a 
text that stays still to be examined and edited. In this way it is like 
writing; indeed, it is writing. 

This is the first of many ways in which the computer breaks 
down the barriers that traditionally separate the preletterate from 
the letterate, the concrete from the abstract, the bodily from the 
disembodied. By straddling these divisions it removes an obstacle 
that has kept many people from crossing from the concrete, body- 
syntonic orality of childhood to forms of competence that have in 
the past been accessible only in literate, abstract, and decorporal- 
ized forms. This applies most directly to Brian. Henry's most obvi- 
ous problems with this crossing are seen in the opposite sense: He 
had moved easily but too thoroughly to the other side and cannot 
easily come back. 

Our culture's supervaluation of the abstract obscures the ways 
in which Henry may have benefited from his exposure to thinking 
about the choreography of movements. Acquiring a feel for creat- 
ing grace and excitement would have stood him in good stead for 
writing a science report, composing a story, or simply telling a 

50 « The Children's Machine 

ways of knowing P ' Um '° a of 

though this in iBelf was ^ . J W «* s ' of course- 

Program computers. Were learain « » 

aJ^rL™tr H Z' s r: ta,ended ,o su8srat - 

Many other taST^'* ~e. 
Perhaps one could sum ,h» m u '° WhaI "Wed. 

ceeded in Jan" "Z^H " * **** * e IeKh « 
•ure in her cZ2m ^2 Z T* C ° mPUKr «* 
ideal. Many children „S h ' Cond,ti ° ns "ere far from 

be stadstically representauve ofTn ^ 15 nM meam IO 

ally represenLdve oTa mode !? , 7**° ~ ro ^P'"- 
Schoofs. The next ii™ ° rm " 8 VC,y tUffere »' 
"immune Z^." " Kp " X ™<** <* tool's 

'h*' ""V**" - "is fount,- and fifth- 

«pe^V™!lh,Th^ *• 
school day in mel,M, ' t " ^ ««V 

gan, he w» «sked aTh", , ^ fom Henni- 

feam who h T , neW Scho ° 1 "* m ™bers of the research 

also knew th* aZe "t 7? " Henni 8»". ^ 

were ^^S^S^^Tl. ^° 

8 wnat ^chard was doing with his 

School: Change and Resistance to Change • 51 

proficiency in Logo. To their surprise, they were told that he was 
not allowed to do it. "But we thought you liked Logo," they said 
to the teacher. "Yes I do," she replied, "and I have my students 
spend a lot of time on it. But Richard already knows Logo. So I had 
him learn something else." 

The story captures one of the chief differences between learn- 
ing at school and all other learning. Generally in life, knowledge 
is acquired to be used. But school learning more often fits Freire's 
apt metaphor: Knowledge is treated like money, to be put away 
in a bank for the future. Something of this way of thinking was 
present in the attitude of the computer teacher at Richard's new 
school. Logo is something to be learned rather than something to 
be used; the students learn it in order to know it; when they know 
it they put it away in their memory banks (which, incidentally, pay 
no interest) and go on to the next topic in the curriculum. In the 
case of computer knowledge, the banking approach is often de- 
fended by the argument that it will stand the students in good 
stead when they grow up and look for jobs that will require 
computer skills. Nothing could be more ridiculous. If "computer 
skill" is interpreted in a narrow sense of technical knowledge 
about computers, there is nothing the children can learn now that 
is worth banking: By the time they grow up, the computer skills 
required in the workplace will have evolved into something fun- 
damentally different. But what makes the argument truly ridicu- 
lous is that the very idea of banking computer knowledge for use 
one day ,n the workplace undermines the only really important 
computer skill": the skill and habit of using the computer in 
doing whatever one is doing. But this is exactly what was given 
up in shifting the computer into the computer lab 

Another way in which computers can be either integrated into 
or isolated from the learning process has to do less with the 
computer as an instrument than with computing as a set of ideas, 
me issue appears very clearly when one contrasts what has come 
to be called "computer literacy" with the sense of the word 
literacy used to refer to someone as a literate person. Computer 

52 • The Children's Machine 

literacy has come to be defined, especially in the context of 
School, as a very minimal practical knowledge about computers. 
Someone who had so minimal a level of knowledge of reading, 
writing, and literature would be called illiterate; the same consid- 
erations ought to lead us to call someone who has an equally 
minimal knowledge about computers computer-illiterate. More- 
over, the difference is not merely one of degree but of one of kinds 
of knowledge. When we say "X is a very literate person," we do 
not mean that X is highly skilled at deciphering phonics. At the 
least, we imply that X knows literature, but beyond this we mean 
that X has certain ways of understanding the world that derive 
from an acquaintance with literary culture. In the same way, the 
term computer literacy should refer to the kinds of knowing that 
derive from a computer culture. 

An illustration of this point is provided by a teaching unit 
designed by teacher Joanne Ronkin at the Hennigan School that 
combines studying the structure of flowers with studying the 
structure of computer programs. The two go together intimately 
and in very simple ways. The student has to make a computer 
program to draw a flower; the structured style of programming 
would suggest dividing the job into writing "subprocedures" for 
the different parts of the flower. The student is then faced with the 
choice of doing this in a way that matches the structure of the 
flower or in a way that does not. In my own programming style 
I tend to be relatively unstructured unless there is a strong reason: 
One such reason would impel me to be very structured about a 
flower program, because I see the "design" of the flower as fitting 
the structured precepts. In fact, I think that the reason for the two 
structures is much the same. A strong argument for modularized 
programs is that they facilitate debugging, and it seems plausible 
to me that the modular structure of biological systems facilitates 
"debugging" in the course of evolution. This is a small example, 
but a pregnant one, of how seeing the world through computa- 
tional concepts leads to insights into familiar phenomena that 
have no direct connection with computers. 

School: Change and Resistance to Change • 53 

The criticism of the computer lab as neutralizing the computer 
is not to be taken as denying that computers in a room apart can 
be used in wonderful ways — so long as the room apart is allowed 
to become the meeting point of ideas that were previously kept 

In a junior high school in Missouri, an unlikely set of teachers 
got together to develop a joint educational project: the physics 
teacher, the physical education teacher, and the shop teacher. 
They intended to develop a workshop for students on robotics, a 
topic with aspects that appealed to each of the three teachers. The 
physics teacher was interested in some underlying theoretical is- 
sues, the physical education teacher in body movements, and the 
shop teacher in machine construction. 

The project had an importance beyond what was specifically 
learned in the robotics workshop. The fact that these three teach- 
ers were doing something together carried a message for students, 
a message that one could formulate much too crudely as recogniz- 
ing that "nerds" and "jocks" might have more in common than 
they think. 

The robotics project provides a simple example of what I call 
second-order effects or systemic effects of the computer presence. 
The school did not spend thousands of dollars on computers 
specifically so that students could have the experience of witness- 
ing a spontaneous alliance among three teachers from strongly 
separate departments. Computers are usually introduced to 
achieve specific educational objectives, and their first-order effects 
are measured by looking at how well these objectives are 
achieved. But, to an extent that varies enormously from school to 
school, the computer presence can come to play a less specific, 
but potentially more powerful, role: By entering the culture of the 
school it can weave itself into learning in many more ways than 
its original promoters could possibly have anticipated. 

The African textiles project mentioned in chapter 1 illustrates 
another important way in which a computer lab can give rise to 
better results than the administration planned or paid for. The 

54 ' The Children'., Mac„ ine 

teacher, Orlando Mihich is one of 

contributed personal time to oZnlT^ 1 ^ k "° Wn who 
1^ outside of school hours : SCSS,0nS in the co ">Puter 

experience. Some of the best'xarnnt? , ** * ^g 
«* Projects came from the ind^St h W 

who refused ^ — ** J^s^r 8 ^ chere 

%T - ent work, the isolation of 

^Ponse of school to a fo^ n J? I ^ ° f immu - - 

Pants were aware that this is what " I " ^ the » 
hC lo ^ ic of ^e process was Jbri^ *** " fa dear *at 
' me With School', ways. The ^^ thi <* back into 

dermining the division of " ' Was 

«to a subject of its own . ««? Sub /ects ; it was turned 

was made the topic of a cu^cullT f ° f " 

"-chartism is not confine^T ^ T But ' ° f — , this 
normalized other subversive nXT " itS ^ Scho °' has 
was the theorist of learning ^ For exam Ple, Placet 

*e P-ject of develop CU ^^ Schoofspawned 

By recognizing such frl^f CUrricuJui «- 

-;wers to the question S « Jed «o «* 
Really searchi m ™ « there no megachange?" by spe- 

~*lb L^S f-d School 
hen stan thinking about ScTooTl " mechanis ™> we can 

^ter change more effectivdy " ^ ** ^ enabie us «o 
o^e more enables us to see 2 ten T * **» a " d Hen T 
way and School's way of landL the **** 

'-ight into this tension to.^L ^Ping 

tt^: r is the of this book - wh * 2 

-ponse to the ^£^5?*?* °* P°««* 

m edUCad °" is » argue that T^^g^"*^ 

very ,dea of megachange is 

w to change . 55 

inappropriate to education- Srh^i • 

examples of meg a chan ee d fi.H 7t " eSSe " tially different ^ 
to ^^uJ^^S^ llkC h SUr f ry ' —rding 
c^e because It 

5Ss ess exami - r 

Time travelers fern a X " ^ ^ bUt " 0t ^change 

ingredients. The act of eatina "s 1 n I ** l ° KC ° gnize th * 
food is cooked in ^LZ^T^ ^ ^ * e 
If there are megadifferences in!!! T 7 ° T not at a «- 

in the technical 8 ' " ^ " ^ ^ and not 

I would agree that learning is a n a t,,r-,i . r 
about the kind of learning Sf h * WC are taJkin 8 

between a mother "d hef babl or^ * * ^ 
know each other. But schoohL i^ ^ tWeen two people getting to 
contrary.- The instituhon of , T " natUI " al 3Ct ^ the 

hxed^culumTn^ ^ ^ «**. 

tends constandy to reduce learnt; ^ P ara P h emalia 

^ teacher to the 2 ^r~-and 

succeeds, for teachers resist the iS^^k^ ^ 
natural human relarionch^ ■ ? rtecnnic,an and bring warm, 

to s^uauon p laces the ^171" ' S 
Poles: School tries to ml,*!, \ ° n between ^ 

cases a seose of ^ ^ h„ h ^ 3 ,eChnid " ni in ">°« 
imemairited SchoS' s cone™ / T a " y the "* Cba ™" "»e 
fore so m e„hennL nB T P KaChin8 ^ Kacher is *«. 
What , dare ca" a ^r""" 1 "" "««- and 

t ecta'e^ri; , :„T„: f , « h T r ducauon ,s the — 

P-es the Mc™ ,Ca '' Z,n8 ' ^ hm the — 

■CeLt ssi 4 : tan 50 grea - a 

another side. Paradox! rr "' n8 ' But ,here is 

raradoxtcaliy, the same technology has the potential 

56 • The Children's Machine 

to detechnicalize learning. Were this to happen, I would count it 
as a far larger change than the appearance on every desk of a 
computer programmed to lead the student through the paces of 
the same old curriculum. But it is not necessary to quibble about 
which change is more far-reaching. What is necessary is to recog- 
nize that the great issue in the future of education is whether 
technology will strengthen or undermine the technicalness of 
what has became the theoretical model, and to a large extent the 
reality, of School. My paradoxical argument is that technology can 
support megachange in education as far-reaching as what we 
have seen in medicine, but it will do this through a process direcdy 
opposite to what has driven change in modern medicine. Medi- 
cine has changed by becoming more and more technical in its 
nature; in education, change will come by using technical means 
to shuck off the technical nature of School learning. 


• • • 


T'HERE was a time when I believed, as many people do, that 
teachers would be the most difficult obstacle in the way of 
transforming School.* This simplistic belief, whose insistent 
presence is in reality a far greater obstacle to educational change 
than the fact that some teachers actually are conservative, can be 
traced back to deeply rooted cultural representations. In my case, 
I remember being impressed in junior high by George Bernard 
Shaw's cynical aphorism: "He who can, does; he who cannot, 
teaches." Someone who "cannot" is not likely to be a constructive 
partner in bringing about major change. 

Culturally shared negative attitudes toward teachers are nour- 
ished by personal experiences. As a rebellious child I saw teachers 
as the enemy. Then, with time, these feelings merged with a 
theoretical position which had the illogical consequence of further 
demonizing teachers by identifying them with the roles that 
School forced on them. I disliked School's coercive methods, and 
it was the teachers who applied the coercion. I disapproved of 
judgment by grading, and it was the teacher who gave the grades. 

*The ideas in this chapter took shape in conversations with Carol Sperry. 

54 • The Children \s M ac „ jne 

teacher, Orlando Mihich is m c 

contributed personal ,me 0 l^T* ■ ' ^ ^ Who 
outside of school hours alowin f °" S * the COm P u ter 
work with the co mputers ^ ng ? SOrae ^dents to 

experience. Some of the be!^ ?" gh ** 3 genuine ^rning 

W — - narrow -T^SSEE?" 

sponse of School to a foTeTn h ! 35 3 ^ of im «™ne re- 
Pants were aware that ^ ° r ™ the pani" 

*e logic of the process wa t^l"? *** * is ^ar that 
' me With tool's ways. The co2t ^ back **> 

dermining the division of " daSSr °° m ^ 

'"to a subject of its own ^ ?° h * »» turned 

was made the topic of a ' ^ ° f cu ™uium ; it 

danism is not confine, " ^ T ' ^ ° f ^ 
normalized other subversive 2" " ^ SchooJ has 
was the theorist of learning ^c ^ F ° r exa <"P'e, Piaget 

Really searching out m ~L "° me gachange?" b V soe 

-gacha^e .IbL'^SS^ f ^ «^ 
hen stan thinking about School i w ' we can 
roster change more efTectiv.,.^. 1 . 75 that wiJI enable us to 
once more enables us to se ^ 1^°' ^ 3nd He <^ 
way and School's way of hand^T ^ teacher ' s 
'"sight into this tension is a cen t 7u Sloping 

is - = ^ e ofthis book wh ^ * 

response to the question ofZ^LT^T ° ne P°«We 
- education is to argue ^T^^T^ 

y 1Q ea of megachange is 

School: Change and Resistance to Change . 55 
inappropriate to education- s^h™, ■ 

examples of megachantd fi^ rJ different from 

to t^ U8fU ^^^ ds kke : u W Surges, according 

change WeVL™ 

rime r^^ h -^ 

food is cookedl^w 8 eSKnUa ">' Ihe same » h o'h=r the 
in the technical dimensions ° al 3nd not 

^TL^£^S h b 3 ^ - * - - talking 
between a inc^^X^ " " ^ 
know each other But sThn > ^ P~P»e getting to 

contrary.- The inltituhon of s7 ■ ^ 3 n3tUral 3Ct " the 

tends constantly to reduce Zr SUCh P ara Phernalia 

^ teacher Jfc ^^^^ rf «^^»d 
succeeds, for teachers r^iA , f ' ° f course . * never fully 

poles: School trte, ,„ „ 77 ° f Knsion beIwe ™ »>» 

fore somewhere a,o„ 8 rhe'conZu^* ^ f t>KK - 
wta ! dare call a true teacher '«hn,c,an and 

Pies the (hie" °„o„ ' 2 '" 8 ' Md ^ ' he ^ — 

crx- atr bem s ° 8reat a -* - 

another side: Paradoxll r T"" 8 ' But ,here " 

raradoxtcally, the same technology has the potential 

56 • The Children's Machine 

to detechnicalize learning. Were this to happen, I would count it 
as a far larger change than the appearance on every desk of a 
computer programmed to lead the student through the paces of 
the same old curriculum. But it is not necessary to quibble about 
which change is more far-reaching. What is necessary is to recog- 
nize that the great issue in the future of education is whether 
technology will strengthen or undermine the technicalness of 
what has became the theoretical model, and to a large extent the 
reality, of School. My paradoxical argument is that technology can 
support megachange in education as far-reaching as what we 
have seen in medicine, but it will do this through a process direcdy 
opposite to what has driven change in modern medicine. Medi- 
cine has changed by becoming more and more technical in its 
nature; in education, change will come by using technical means 
to shuck off the technical nature of School learning. 



T'HERE was a time when I believed, as many people do, that 
teachers would be the most difficult obstacle in the way of 
transforming School.* This simplistic belief, whose insistent 
presence is in reality a far greater obstacle to educational change 
than the fact that some teachers actually are conservative, can be 
traced back to deeply rooted cultural representations. In my case, 
I remember being impressed in junior high by George Bernard 
Shaw's cynical aphorism: "He who can, does; he who cannot, 
teaches." Someone who "cannot" is not likely to be a constructive 
partner in bringing about major change. 

Culturally shared negative attitudes toward teachers are nour- 
ished by personal experiences. As a rebellious child I saw teachers 
as the enemy. Then, with time, these feelings merged with a 
theoretical position which had the illogical consequence of further 
demonizing teachers by identifying them with the roles that 
School forced on them. I disliked School's coercive methods, and 
it was the teachers who applied the coercion. I disapproved of 
judgment by grading, and it was the teacher who gave the grades. 

*The ideas in this chapter took shape in conversations with Carol Sperry. 

58 • The Children's Machine 

Yet I c ertainly had grounds in early experience for , m 
thetic view of teachers. ex Penence for a more sympa- 

Like most people with generally bad memories of ^h™i r u 

-Thou ^ , nvent dJf^L^saLs*": 

throw them away before dinner ■• 7 1 Tl bre akfast and 

that I am indebted » him F™ ', ed l " m ' a " d ** «*» "°» 

•he time, and until receriuy ^ZZST* ^ " 
leaving my andteache, prI|udke^fenSe 3 *" eXCePti °"' , " US 
who say: -Me' Why some „7 I , * e racism of th o« 
effect wL not , Tmmk bene^ „7 ? " 71,5 "« 

■eaeher, he's a "afmen^h , h'^ '° "* " DalS >" s "° 

School tha, disguises memento™" *** * * 

opS^Tp^ttS ° f ** hm, 

tedd *ei,perso^Xof* cZ P T„, *" ^ «* 

They were frustrated S ™ . WaS n °' ^ for 

w°*wiU,rm~mpu^svr T ^ "«* tad » 

among severaTctZ™ " a " d tad to sharc *em 

e cverai Classrooms, opportunities to devel™, ,t 
compute, k„„ wledge were 0,m 

spouse often snatched away the succej « acTTp * 
the logo they had in those days loots sarftoV, , en 

back on „ from the perapecdve tf^lSZT ' J** 
language. More recent versions of TZ , d ?* dc ° f » OT «l>°f *t 
intuitive and flewhk I , u 8 " re far more user-friendly 
neering mac^^l^ ' ^ °< — <*- 
classroom environmenTX ri, ££££ ^ ' 
understanding riie force for chanL taem to * f ** 

Teachers . 59 

as a vehicle through which the readers come to understand k 
the author thinks. M«* to ™ worked for ^'te onn 
direction as well. e °PP os «e 

I had not written the book with teachers in mind- at most r 
imagmed it being read by a small vanguard among them S Zt 
the estimated number of teacher readers climbed imol °ll 

Zb r: h 1 1 perturbed what dw they ,ike * ™y Si 

unde-nd ^ *«" ^ °™ ™* ' « - 

Fortunately, the book also helped me find answers to the ques- 

ce v d" ™ 3 ~ into the world of teachers I 

yeZ^s ^u K tterS fr ° m teaChefS tellin ^ me ab ™ their 
yearnmgs and hopes, their plans and resentments. I was flooded 
with mvttauons to give speeches and seminars, visit schooTand 

u P :deXdlTf tS h M ^ ° ffered 3 *«" o 
understand what teachers were expressing in their experiments 

' SclT^T / S 1 ^ S °' my ide *ation of "teacfe™ 

bXrof for^ b ° th 3 Uberatin « Sense ** ^he 

poS and atTe ^ ^ faV ° rab,e » Change than 1 had ~P- 
,nternl i 53016 ^ 3 " chaUen »= to understand the 

en u 8 W3yS t0 SUpport the evolu "on of these cur- 

make to promote educational change 

lootin^f 81 " 011 ^ t0 Underetandi "8 these currents, I begin by 
ookmg at a story recounted by education writer Fred Hechin g er 
n a sorely missed New York Times column. I cannot fmale a 
teacher who will not hear in the storv the Pr h. 7 & 
experience. ^ ° f Some Pe iso ™l 

che™^ dif rt 3 , NeW ^ SCh001 dr ° Pped in to ""en to a 

Sd ^he r r was br,iiiant - The Prind P al — - 

tnrailed^ After the class he congratulated the teacher on a superb 

teach/ Tf ^ 3nd the " to S6e his <~ P - The 

teacher replted that since he knew this materia, so well and cared 

60 • The Children's Machine 

about it so much, he didn't think he needed a lesson plan. The 
principal clearly had no complaint about the lesson itself, but the 
teacher was guilty of not following procedures and had a letter of 
reprimand placed in his file. 

There is more than one way to read this poignant account of a 
system defeating its own purposes in the attempt to enforce them. 
One can take it as a satirico-comic account of a run-in between an 
overzealous supervisor and a naive worker, the former ridicu- 
lously literal-minded about a minor transgression of the letter of 
the rules and the latter refusing to understand the importance of 
appearances, which could have been saved by writing a token 
lesson plan. On this reading, the story is only incidentally about 
School; it could be matched by bureaucracy stories from other 
walks of life. 

On another reading, however, the story touches the nerve of 
what School is really about. It evokes tensions between a warm 
idea of School as a nurturing place for children and a chilling idea 
of School as a machine to perform laid-down procedures. It 
evokes yearnings for teaching that will help us fall in love with 
knowledge, and frustrations at being made to learn lists of facts, 
loved or not, that experts have decided must be known. 

The choice between these readings of Hechinger's story reflects 
the central question about education: Is the trouble with school a 
superficial one that could be fixed by a good dose of good will 
and common sense, or is it a deep flaw in the foundational as- 
sumptions on which the entire system is built? Is School's malady 
a cold or a cancer? 

The meaning of these two views is brought out by comparing 
Hechinger's incident with my central example from the previous 
chapter. School has evolved a hierarchical system of control that 
sets narrow limits within which the actors — administrators as well 
as teachers — are allowed to exercise a degree of personal initia- 
tive. Neither side ever fully accepts these limits. The Hechinger 
story shows a border skirmish in a permanent struggle for power 
in which participants constantly test their strength without actually 

Teachers • 61 

challenging the system itself. The seeds of a sharper challenge 
were present in the decision to allow Brian and Henry to spend 
their time on computer choreography. The chemistry teacher 
could, had he wished, have written a token lesson plan, as many 
of his colleagues routinely do. Thelma did not have this option. 
There could not be a lesson plan for the simple reason that there 
was no "lesson." 

Thus the original decision about how to use computers 
placed the teacher on a collision course with School's system of 
control: As soon as she decided not to control the students, she 
took away School's established way of controlling her. The 
question has moved from how power is distributed within the 
educational hierarchy to whether hierarchy is an appropriate 
mode of organization for education. There are activities where 
hierarchical organization is obligatory: The military is an obvious 
example. At another extreme there are activities where any sen- 
sible person would judge hierarchical organization to be ab- 
surd, for example, in poetry or painting. In other areas there is 
room for choice in the balance between hierarchy and its op- 
posite — for which I follow Warren McCulloch in using the name 
heterarchy, which suggests a system in which each element is 
equally ruled by all others. Where on this spectrum between 
soldiering and poetry should one place the organization of a 

There is a danger of thinking about this as a "management 
problem" that a school could address (and many do) by bringing 
in a general-purpose expert on how to run organizations. But 
injecting a new management plan into an otherwise unchanged 
School is like injecting computers or a new curriculum while 
leaving everything else unaltered. The foreign body will be re- 
jected. School's hierarchical organization is intimately tied to its 
view of education and in particular to its commitment to hierarchi- 
cal ways of thinking about knowledge itself. What one will con- 
sider to be the proper place for School on the heterarchy- 
hierarchy scale of organizational forms depends on the location of 

62 • The Children's Machine 

knOW ' ed8e °" ^ ~^'-ch y sca,e of 
A caricatured hierarchical theory of knowledge and of school 

Per day. A tale calculanon shows that 180 days a year for 12 years 
be suffid <™ >° 8« 43,200 atoms into their Lda-buT^ 
operanon will have to he we» organized, for while Tote over! 

charge ^hereaher callers ^ fit ~Z 
b*nks. The pro b ,e m £ qua , " 

«y that there are hierarchical relations among the atoLl FataTfJ," 
*™ed to match the htarchy of kn JledgTl^ IT" 

~riXr:'dTh - cssi 

Such a *I T ' Um by '"POtaKndenn. 

se^ C ?e.Th n0b °f "kT 1 " SUbSCribe M m a literal, where to place bricks; and the adminisdatn 52££ 

Teachers • 63 

would have been severely remiss for allowing her to do so. But 
she was not being lax, lazy, or irresponsible. Teachers who give 
so much autonomy to their students are thereby declaring their 
belief in a radically different theory of knowledge, one that entails 
far more work for them as well as for their students. 

My use of the term "theory of knowledge" rather than 
"method of teaching" is deliberate. Progressive educators do not 
see themselves as offering an alternative way for students to 
learn the same list of items of knowledge. They value a different 
kind of knowledge. 

For example, I occasionally use an elevator that has a security 
code. One has to key in a four-digit number before it will move. 
Since the code is changed frequently and I use the elevator only 
rarely, I usually remember each new code in a vague form. 
"There's a 17 and a 34," I say to myself; "perhaps it is 1734 or 3417, 
or maybe the numbers are 71 and 43." I make a few tries and the 
elevator moves. I think that's fine. It works. In school, however, 
I would fail the elevator-skills test. This is a trivial example of an 
important phenomenon that I call knowledge-in-use. When 
knowledge is doled out in tiny pieces, one can't do anything 
except memorize it in class and write it down in the test. When it 
is embedded in a context of use, one can push it around and fix 
minor bugs such as reversing the digits of the elevator code. 

I am not suggesting that knowledge-in-use is the essence of 
progressive epistemology or even that every progressive teacher 
would accept this principle. I am using it here only as an example 
of a "different kind of knowledge." What teachers who reject 
School's philosophy of education actually believe varies widely. In 
fact, every teacher should be encouraged to go as far as possible 
toward developing a personal style of teaching. A less specific 
metaphor that I used in Mindstorms, however, does seem to cap- 
ture a widely shared element well enough to provide a framework 
for looking more closely at the aspirations and problems of pro- 
gressive teachers. The basis of the metaphor was an observation 
about the idea that children display "aptitudes" for their various 

64 • The Children's Machine 

school subjects. It is thoroughly embedded in our culture that 
some of us have a head for figures while most don't, and accord- 
ingly, most people think of themselves as not mathematically 
minded. But what do we say about children who have trouble 
learning French in American schools? 

Whatever the explanation of their difficulty, one certainly can- 
not ascribe it to a lack of aptitude for French— we can be sure that 
most of these children would have learned French perfectly well 
had they been born and raised in France. Perhaps they lack an 
aptitude for learning French as it is taught in American schools 
but that is a different matter altogether. In the same way we have 
no better reason to suppose that these children who have trouble 
with math lack mathematical intelligence than to suppose that the 
others lack "French intelligence." We are left with the question- 
What would happen if children who can't do math grew up in 
Mainland, a place that is to math what France is to French? Man v 
teachers accepted the challenge to build something like a Math- 
land in their classrooms, and took Logo and its turtle as building 
material. Thelma's classroom shows in a general way how many 
went about doing this. Following this metaphor, one can think of 
Brian and Henry as being in Mathland; what they were doing with 
the computer was more like learning French in France, while what 
happened in the regular math class was more Uke learning math 
as a foreign language. In these computer contexts, as in learning 
French in France, the learner can begin by knowing something in 
a very fumbly sort of way before it becomes established. In the 
math class, where knowledge is not used but simply piled up like 
the bricks forming a dead building, there is no room for significant 
experimenting. s 

Many progressive teachers might have doubts about whether 
creaung a Mathland is really feasible and hesitations about what 
inconveniences it might bring if it is; but leaving aside practical 
considerations, it seems obvious to them that learning French in 
France and math in Mathland is in principle a better way than 
those of the traditional classroom. 

Teachers • 65 

The immediate consequence for the practice of teaching is the 
one I have already noted. The learning of a dead subject requires 
a technical act of carving the knowledge into teachable bites so 
that they can be fed to the students one at a time by a teacher, and 
this leads straight into the traditional paraphernalia of curriculum, 
hierarchy, and control. By contrast, Brian and Henry were able to 
find their own way to structure their knowledge with only occa- 
sional advice. Learning-in-use liberates the students to learn in a 
personal way, and this in turn liberates teachers to offer their 
students something more personal and more rewarding for both 
sides. But this prospect does not come without problems, and 
some teachers will see it more as a threat than as a liberation. 

Thelma's rewarding feeling that she had exercised a creative 
(and unintentionally subversive) act in setting up her plan for 
computers brought psychological as well as bureaucratic risk. 
School's definition of roles and procedures restricts the teacher 
but also offers protection, as we see in the following story whose 
main features I have heard from many who have taken the same 
course as Thelma. 

The following is a reconstruction of what I heard from Joe, a 
fifth-grade teacher: 

From the time the computers came I began to be afraid of the 
day my students would know more about programming than I 
ever will. Of course, at the beginning I had a big advantage. I 
came fresh from a summer workshop on Logo, and the students 
were just beginning. But during the year they were catching up. 
They were spending more time on it than I could. Actually, they 
didn't catch up the first year. But I knew that each year the 
children would know more because they would have had expe- 
rience in previous grades. Besides, children are more in tune 
with computers than we grown-ups. 

The first few times I noticed that the students had problems 
I couldn't even understand, let alone solve, I struggled to avoid 
facing the fact that I could not keep up my stance of knowing 

66 • The Children's Machine 
more than they did. I was afraid that giving it up would under- 

£— £2* H 3 teaCher Sit ~came w^ 

Eventually I broke down and said I didn't understand the prob- 
lems-go dtscuss it with some of the others in the c ass who 
might be able to help. Which thev did AnW ; , V h ° 
together me kids cJd figulufa J£E Nowthl aml^ 
hmg 1S th at what J was afraid Qf tumed "J^Sf 
I no longer had to fear being exposed. I was. I no^on«er had I to 
Pretend. And the wonderful thing was that I 3^at mv 

IS? k u° W ^^"8 in other subjects as well Whafa 

mIS My ^ ^ 

myself. My class has become much more of a collaborate 

community where we are all learning together. COUabonU,VB 
Reflection on this story will show that there is no simple answer 

of TteC Hwt ZT" herS fit thC ° ptimistic desc «P«on 
or ihelma? How far would they take these ideas? How much efl™, 

and sacrifice would they makeP My description gZrke^Z 

fears and the ambtvalence that Joe shares with most of the teach 
ers who were drawn to experiment with computers Z an 
ment of change. Joe embarked on th~ mpUters as an lnstru - 
tion. He did not fulv adT l^™ 1 with 

have andwhl h What P Iobl ™ he would 

nave, and when they came up he hesitated. Events turned out well 

ba.ance *. can *«S^^"J*?* °» ' 

Teachers • 67 

the adverse factors: Only by understanding them can we craft 
sensible strategies for the future. By the same token, they give little 
grounds for comfort to those who still predict that computers do 
not have a significant future in education. 

Despite his doubts, Joe went further than the others I have 
mentioned so far. Hechinger's chemistry teacher tried to express 
his own intellectual enthusiasm in his teaching; Thelma tried to 
create an environment in which children would develop their 
own enthusiasms; Joe took a further step by explicidy formulating 
the idea (which the others may have had tacitly) of joining the fun 
as a co-learner with his students. The progression is psychologi- 
cally understandable. Wanting to learn is a basic human desire, 
and being with children who are doing it while being deprived 
oneself is like being a dieter watching the diners in a fine restau- 
rant. Why don't all teachers do it? 

Many aspects of School block teachers from the fulfillment of 
functioning in a class as co-learners. The mundane matter of 
schedule is most often mentioned if one asks progressive teachers. 
They say that there simply is not enough time. I think Joe shows 
the fallacy in this explanation, however. There would indeed not 
be enough time for him to keep everything else and also get in his 
own learning. But he had the courage to implement a plan with 
a better chance of working: He changed the life of his class in such 
a way that students could give as well as take, and his learning was 
not competitive with theirs but contributed to it. To do this he had 
to face something that it took courage to admit: Most of the work 
he made his students do was too boring to entice him to join in! 
The computer changed the situation because it itself is an interest- 
ing object to learn about and because it added dimensions of 
interest to other areas of work. 

What I actually saw Joe doing with his class involved a much 
broader range of learning than the technical aspects of computer 
programming that had been the object of his fears. Some of his 
students were doing work like Brian and Henry, but most were 
engaged in projects of a very different kind in which mathematics 

68 • The Children's Machine 

was integrated into fact-oriented subjects such as history or sci- 
ence. An aspect of these projects was something I first saw in the 
work of a fourth- and fifth-grade teacher at the Hennigan School 
in Boston. 

Before computers entered her life, Joanne had developed a 
project as part of her classwork on human biology. The topic of 
study was the skeleton, and her style of handling it was to ask the 
students to choose a bone and make a report on it. When the 
computers came she simply did what she had always done, except 
that the students knew enough Logo by then to make their report 
on the computer screen instead of using pencil and paper. In one 
sense nothing changed except for a shift of media. But the shift 
had consequences. One of these was related to the fears ex- 

This picture was generated by a Logownter program written by 
four fourth-grade students. 

Teachers • 69 

pressed by Joe. The computer is an open-ended technical device 
that incites at least some students to push their knowledge to the 
limit to enhance the project through an unlimited variety of "ef- 
fects"; thus learning more about computer techniques becomes 
part of the project in a way that had not happened with pencil and 
paper. This might seem to distract from the "main purpose," 
which was studying biology. It did not: Thinking about represen- 
tations on the screen produced a richer engagement with the 
skeleton than had been usual in the precomputer days. The skele- 
ton illustrated, the collaborative work of four students, shows 
several features that are typical of what happens in a computer 

First, the students transformed the assignment of representing 
a bone into one of representing the entire skeleton, a goal that was 
made possible by the fact that the computer allowed much better 
conditions of work: Parts made by the collaborators could be put 
together more easily. A close look will show that modules could 
be used in several places, and most important, changes would be 
made easily without the messy process of erasing or the tedious 
one of starting over. Second, these same working conditions facili- 
tated a double intention that is clearly visible in this object: The 
figure was made with an eye to visual aesthetics as well as to 
scientific accuracy. This raises challenging issues about the nature 
of knowledge and the criteria for judging it. I would call it an 
epistemological responsibility of the teacher to enter into discus- 
sion with these students (which in fact I had the privilege of 
doing) about what was sacrificed in each for the sake of the other. 
There can be no absolute answer, but there can be articulate and 
thoughtful discussion. 

The issue of science and aesthetics is just one of many that 
make a different kind of demand on — and offer a richer kind of 
opportunity to — a teacher than is usual in a science class. 
Whether this is seen as a demand or as an opportunity, it cer- 
tainly requires knowledge and sophistication for which there is 
no place in the course catalog of the typical school of education. 

70 • The Children's Machine 

Where can teachers find help in developing themselves in these 
directions? What kind of development would help them? 

To define this problem, which may be the most important of 
all those facing the adoption of computers in education, it might 
help to review some of the obstacles faced by teachers who try 
to find a solution. The most brutal of these simply prevents the 
interesting situation from arising. The designers of the skeleton 
had access to computers for about one hour a day, and their 
regular teacher had the freedom to use this time as she wished 
Thus they and the teacher could be immersed in the project 
sufficiendy for interesting issues to come up and be dealt with in 
an interesting way. 

The odds are against anything like this happening— though it 
is a tribute to the amazing resilience of students and teachers that 
it sometimes does— when students have forty minutes a week of 
computer lab and learn about word processing, data bases, and 
what's in the computer, as well as "do a little Logo." A second 
obstacle is the concept of teacher training. Although the name is 
not what is most important about this concept, it is curious that 
the phrase "teacher training" comes trippingly off the tongues of 
people who would be horrified at the suggestion that teachers are 
being trained to "train" children. The phrase makes me think of 
toilet training, basic training, and tiger training. I know that the 
word training is often used for respectable kinds of learning. For 
example, I said in the second chapter that I was trained as a 
mathematician. But justifying "teacher training" in this way feels to 
me— and to quite a number of teachers I know— like justifying 
the use of the pronoun he on the grounds that it embraces 
woman. On purely abstract linguistic grounds both usages are 
"correct," but in both cases what is involved is not an issue of 
syntax but one of ideology. Why the asymmetry? Why do we talk 
about teachers and children so differently? The answer brings me 
back to my main theme: School does not have in its institutional 
mind that teachers have a creative role; it sees them as technicians 
doing a technical job, and for this the word training is perfectly 

Teachers • 71 

Whether or not one accepts this analysis in general, it is hard 
not to recognize its truth in the kind of preparation School gen- 
erally considers appropriate for computer teachers. In many 
school systems, what the teachers who will use the computers 
are offered in preparation is quite appropriately called training 
for it consists of a small number of two-hour sessions, mis- 
named "workshops" or "seminars," whose goal is to impart 
technical skills. To highlight the limitation, it is worth looking at 
two examples of providing better conditions for teachers to 
learn and grow. 

About eight years ago I conducted a summer workshop on 
Logo for a small group of teachers. I was a little nervous because 
I suspected that one of the participants was there not out of 
commitment to learning Logo but because she was under orders 
from a principal who wanted a computer project in his school at 
a time when that was still something exceptional. I knew that a 
single participant's bottled-up resentment at losing summer vaca- 
tion time could poison the spirit of the group, even if the others 
had come out of a personal desire to learn. 

One of my preferred styles of working with such a group is to 
: propose a form of project sufficiendy open to allow very differ- 
Hpt approaches and sufficiendy restricted to allow the different 
approaches to be compared. In this workshop I proposed that 
^everyone write a program to represent some aspect of the no- 
i*ion of "village." Programming the computer to draw a village 
;pn the screen presents itself as a good theme for beginners to 
praise techniques of programming. One can start by writing a 
procedure to draw a single dwelling; once this is debugged it 
>can be used as subprocedure for a superprocedure to obtain a 
sgroup of identical dwellings; and having obtained a product 
f ne can go on to introduce variability and add all manner of 
mils and details including animation, text, and hypertext. From a 
teaching point of view, it has the advantage that students can 
«op at different levels, matching their technical abilities and 
personal tastes, and yet all have something to show for 
We work. 

72 • The Children's Machine 

As the days went on, my fears did not seem to be founded 
Everyone was caught up in the activity. I was especially relieved 
to observe that the member of the group I had thought would be 
most difficult seemed hardly able to contain her excitement Z 

zz 0 :T sion r°u she bubbied ° ver ^ **» 

she would use what she was learning; even when she was work- 
ing at her computer she would exclaim from time to time that she 

1.1 L J, ^ ° f evaluation . *e workshop was going 

well My educational objective for my students (the teacher * was 

das wTT! g ° ^ PdnCipleS ° f P^—ing, and the 
class was makmg reasonably rapid progress in this dfrection- 
and showing enthusiasm as well curection 

wronTf 1 3 na88ing ***** that som «hing was 

Zntr C °H T ^ fin8er °" What * Was a * 
commouon broke out in the workshop. One of the other partfci 

Panu . apparently had the same misgivings as I did but m^e 

sTonfoftfr 56 " ^ r blCm - ^ ^ ^ 
Z " mU " ered ' " F ° rget the [-Pletive] chil- 

tZ sZJT'T ° f ^ in thG r °° m was electric- Some 
suoLrtn , Pr ° teSted; ° ne ™ edia tely responded with a 

^upporung remark. I was at first taken aback and then realized 
Aat the outburst captured what had been troubling me The 
discordant element had been a sense I couldn't yef artLhL 

Z sgsri thought of themseives - - ch ~" 

mg rather than as learners. Their awareness of being teachers 
was preventing them from giving themselves over fultyto^ 

a"s ThTl 8 'k" T l * C ° Uld bdng them as P rivate tad 12- 

Z2Z££S£? way of teachers — g — 

I w^freeri 3 ^^ 1 S ° me£hing 3ikeJOe ' S sense of liberation. 

neX seeker * *°" WaS a " d 

Mv freedom ,n 8 , Unty m ^ te3CherS ' exclama ^s of delight. 
My freedom allowed me to look more closely at what the individu- 

Teachers • 73 

als were doing with their programming, and soon I noticed a 
striking difference in style. Some were constructing the houses by 
putting together clean geometric shapes, in the simplest case fol- 
lowing the example I had used in Mindstorms.- A "house" can be 
made by putting a triangle on top of a square. One of the partici- 
pants seemed uncomfortable with these shapes. Perhaps they had 
bad associations with School math or perhaps her personality 
biased her toward fuzzier things. Whatever its origin, the discom- 
fort led her to pick up an idea from someone else's failure to make 
a neat geometric pattern to represent a flower garden. It came out 
as a wiggly line that might have been a failed flower garden but 
was just the thing to turn into smoke rising from the chimney of 
the house. After a while all the houses had smoke in varying 

One thing led to another. The smoky effect could be adapted 
to draw clouds floating over the village and, with a little more 
adaptation, to draw trees and other less square objects than 
houses. Sometimes very small actions by a teacher can seed 
growth in a class. One that became important in this workshop 
was naming the emerging programming style. I dubbed it 
"smoky programming" and contrasted it with "hard-edged" 

The immediate effect was to encourage the original smoke 
maker. At this point it was an individual act involving teacher 
(myself) and student. Gradually it turned into something more 
social. Naming styles became a habit and encouraged personal 
pride in them; they became something to discuss and something 
to own. A vocabulary developed for talking about them, a sense 
of values for respecting others' styles even while taking pride in 
one's own. 

5 In short, a process was under way that I would call the begin- 
nings of a microculture. Talking about styles is an excellent seed 
for the development of a learning culture; it contributes to the 
richness of the immediate learning but also allows the benefits to 
now into other areas, since styles can be recognized across a 

74 • The Children's Machine 

variety of different contents and activities. All learning benefits 
from talking about it— so long as the talk is good— and compar- 
ing styles is one of the best conversation starters provided that the 
differences are clear and the participants authentically respect the 
styles of others while defending their own. But for the talking to 
be good it must be both rooted in the real concerns of the partici- 
pants and supported by knowledge and experience. 

The issue of the contrast between the smoky and the hard- 
edged styles of programming was indeed very well rooted. It was 
not just a simple difference of style, though I was trying to pro- 
mote a culture in which any difference would in fact be respected; 
on the contrary, the issue has been central in debates about alter- 
native epistemologies. The hard-edged style is closer to the ana- 
lytic, generalizable ways of thinking valued by the traditional 
"canonical" epistemoiogy, which has come under fire from femi- 
nists as androcentric, from Afrocentrists as Eurocentric, and gener- 
ally from many on the political left as representing the thinking of 
dominating groups. Indeed, research by MIT sociologist Sherry 
Turkle and myself shows that it is more likely to be the preferred 
style of white males. This is enough to make it very relevant to 
teachers, but in fact there is another aspect that makes it even 
more direcdy so. Moving from the hard-edged to the smoky style 
involved a step away from an abstract and formal approach to one 
that invites all the words that Piaget (taken as representative here 
of a far wider span of psychological thinking) would attach to the 
thinking of younger children: concrete, figural, animistic, and 
even egocentric. 

Thus the issue is rooted in the teacher's concern about what 
kind of thinking is appropriate for children— but in such a com- 
plex way as to lend great importance to the second criterion for 
good talk about learning: the necessary knowledge and experi- 
ence. Much more than "training" is needed for teachers to develop 
the ability to benefit from the presence of computers and to bring 
this benefit to their students. 

It is instructive to note how a small Central American country 
has been able to handle this problem in a way that puts most 

Teachers • 75 

North American school systems to shame. I would suggest that 
this is largely because the country classified itself as a "developing 
country" and made this an advantage compared with countries 
that see themselves as "developed" — and so presumably have 
nowhere further to go. One moral of the story is that we might all 
do better if we dared classify ourselves as "developing." 

In 1986 Oscar Arias was running for election as president of 
Costa Rica. The same mentality that would enable him to win the 
election, launch the peace process in Central America, and gain 
the Nobel prize was reflected in an election promise to take steps 
toward ensuring that Costa Rican children think of themselves as 
belonging to the modern world and not as Third World outsiders 
looking on longingly. One of his steps would be to bring comput- 
ers into all the elementary schools of the country. Later I shall have 
several occasions to refer to aspects of what turned into a project 
with many exemplary features. Here I focus only on how the 
project did more than "train" its teachers. 

For better or for worse, a decision was taken to invite corpo- 
rations to submit complete plans, not only to supply and main- 
tain computers but to determine the educational content, 
teacher preparation, and the evaluation process. This was a 
commercial plum involving many thousands of computers, so it 
was not surprising that fourteen companies submitted bids. IBM 
brought me in as a consultant and followed my advice to submit 
a plan that was exceptional in the proportion of effort devoted 
to the preparation of teachers in advance and their support dur- 
ing the project. This may not have seemed to make sense in 
terms of trimming prices in a competitive bid; but at the head of 
IBM's Latin American Education group was an energetic, intelli- 
gent, and not at all bureaucratic woman. Alejandrina Fernandez 
persuaded her superiors in the corporation that IBM could af- 
ford to lose money in the first year of this project. It turned out 
that paying attention to the role of teachers won her the contract 
and has led to a successful model that has been used in half a 
dozen Latin American countries. 

The Costa Rican government created a foundation to oversee 

76 * TH£ C »"-^en's M ACH1N£ 

protLTfproiect froZtf^nhl* g ° Vemment h ^ing the wit to 

hat the mode of use should be as ^77' ° negrou P ^"ed 
Many of the teachers in the runL di!2 u 38 **** 

with technology and J little experience 
These teachers, it was argue^ould t !" tec ^. 
u^ng the computers thai S^f 6 .^ * any mode of 
***d for using CAI soft^^jt^ ^ Thus «* group 
would probabJy haye zZ ; *T<r W ° n the co « 

on and the teacher does > Zln^ ^ b Swi ^ed 

Aing is automatically done ulrt l0ad 3 ^"e-everv- 

of theothergroup, though heyd ZZT- ^ ^ 
was to make it as hard as 7 PUt * in these words 

^sra Rica, underthe] c.^^!^ f^^- In the end 
an exempli pr0 gr arn in Z * 2^°^^^ 
whom indeed had no technTca, L ^ teaCherS ' most <* 

« Logo and derived a ^711^°^' kuaed to P*W*n 
^ves and their country bZzsZn^ * *^ 

enced as challenging mode™ S *" n ^ SOme ^ng that was experi- 

This is in' i^iST* f ° r Pe °^ 

adopted by rnany^e^^ ^ast with the position 

^^'^^ L08 ° iS " edU - 

*** * was obvious to 7Z2l r SUCh measu —ents, 
o learning took place "ZZ^ZV""**'™* 
obvtous that this happened beL^T' * " WaS a,most as 
, £hat ™h more wasYnvdve^Z P3rtid P atin 8 teachers felt 
Naming basic skills. They wer * J dement in 

** wil, to appropriate LT^S? ' 3SSerti ° n of 

"on against a view of te^h;„„ . 8; a P rofe ssional asser- 
*»■ assernon a 8 ai„ st ' Jr *»™ i a ^. 

°' co «ntry as under- 

Teachers • 77 

deTfoff , Ma " y ° f ' tam alS ° mak '" 8 »" "^nion of ge „. 
worn n a„d7 SCh ° o1 •»<*»« 

rxr*; = had tad ,he - - 

The Costa Rica project showed in a specially clear form the 
computer playing a role in identity formation by teachers and 

ofTchlr t T drC,e t0 ^ ^ ° f ^ -presentations 
ot teachers. In a conversation with Oscar Arias, who asked me 

what I thought was the most interesting aspect of the projecH 

~°d 1 h 1 h3Ve bCen ^ ^ ab ° Ut -achers P Ama"e 
meat and delight were written all over his face when he heard me 

talk about how much effort teachers had put into the project He 

on'hel W t at hC h£ard 3bOUt ^ in »° pS wa 
on the lines that they wanted more money for less work, and told 

z a7w^ a ,tft h r s tha H his computer project had " 

bel oZ lf Presidential palace feeling proud to have 

what Z L " 7 P T nity tCaCherS t0 Sh ° W themse ^es for 
what they are and to become a little more 

proTecfoariof 'TT^ ^ °PP°™*Y «° make the 

project pan of a developmg sense of identity, the Ptvgrama Infbr 
rnauca MucaUva has another feature that makes it ZTopTei 

Ipu^Th^ " 3 COmpr ° miSe bCtWeen the 

uTclassr W " imP ° Sed by finandal c -^aints3 and 

where the ^ d ° 8 ° l ° 3 Se P ara * room 

teacher! TT ^ ,OCated ' bUt ** re * uIar ^sroorn 

too fo fn th H k t em " M ° reOVer ' the teacher lea ™ w^ them, 
too, for ,n the lab there is also a computer teacher who has had 

22 ^development (to a degree that is rTeTen in 

also a! L T ^ T ntdeS) ^ ° nly 35 3 technical -P-t but 
also as the interpreter of a culture of learning 

Another version of the compromise had been the goal of a 

^ ^ ^ reS£arCh fifSt at the P- 

«fn 7ln r « S ^ thCn in Pr ° jeCt Headli8ht at th e Hexmi- 
m School m Boston. The model, which needed more resources 
than Costa R lca had been able to afford-though far less in 

78 • The Children's Machine 

proportion to the national wealth of the two countries— originally 
incorporated three essential principles. First, the number of com- 
puters would be sufficient for every class to spend at least one 
period each day with its regular teacher, when every student could 
have full access to a computer. Second, although any educational 
software might be used on occasion, the primary use of the com- 
puters would be based on the assumption that everyone, students 
and teachers, would be able to program the computer in Logo 
from the outset. Third, all the teachers would have not only suffi- 
aent expertise but also sufficient freedom of choice to use the 
computers in a manner that would express their personal styles of 
work. Later, a fourth principle grew out of these three when the 
Gardner Academy, a largely Latino inner-city elementary school in 
San Jose, developed its own implementation of the three princi- 
ples under the name Project Mindstorm. This fourth principle 
asserts the advantage of the explicit development from within the 
school of a unique indigenous learning culture and philosophy of 
education. The project's name marked an intention to adopt my 
ideas; its divergence from what I had described myself was, in my 
view, part of a confirmation that it had succeeded. In education 
the highest mark of success is not having imitators but inspiring 
others to do something else. 

The project was created by the Technology Center of Silicon 
Valley, which let the project evolve without interference after it 
had selected a school and a director. The director was Carol 
Sperry, who came to computers after many years as a classroom 
teacher. I believe her own experience helped to empower the 
teachers in the project to create a culture in the school and to see 
it as thetrs She was not someone who came from a university or 
a school bureaucracy to tell teachers what to do with computers. 
Because she was a teacher herself, and did not feel answerable to 
anyone outside the school, she could ask the other teachers to join 
her in "putting herself in the disk drive along with the Logo disk." 
The intensity of the personal involvement created an unusually 
strong culture of teachers, and this in turn gave several of the 

Teachers • 79 

teachers the intellectual confidence needed to nurture an unusual 
culture among students. An example will illustrate the point. 

When I was discussing Brian and Henry, I quoted a student 
who talked about putting "grace" into his computer graphics. The 
student, who was from Project Mindstorm, explained that he 
wanted to grow up to put art and mathematics together. What is 
unusual here is not the fact that a student would say this, but 
rather that the teachers could cope with this way of thinking about 
mathematics. The special demand on the teacher is seen in an- 
other light: As long as there is a fixed curriculum, a teacher has no 
need to become involved in the question of what is and what is 
not mathematics. But here the teacher was willing to take on what 
would be considered a philosopher's question, and to become 
involved in serious discussion with students and with colleagues 
about whether this student's activities — which looked very dif- 
ferent from any math in the curriculum, as the figures on page 80 
show — were nevertheless mathematics. 

In this chapter my thinking has been conceptual: I have presented 
a concept of School, a concept of the teacher, a concept of the 
bureaucrat, and a concept of struggle. I conclude here with some 
more pragmatic remarks on strategy for change. 

What can be done to mobilize the potential force for change 
inherent in the position of teachers? First I must make some 
qualifications. The conflict I have described is one of idealized 
principle. In order to bring out the ideas, it comes too close to 
presenting an image of pure angels engaged in a holy war with 
evil demons. Real teachers have mixed positions. Everyone who 
has grown up in our society has internalized something of 
School's way and teachers are no exception. At the same time, 
most school administrators were once teachers and continue to 
share some of their yearnings. Hechinger's story is not about a 
wicked principal; it is about the role of principal: the office, not the 
Person. Carol Sperry has written about "contradictions" even in 
teachers who think of themselves as militantly working for 

80 • The Children's Machine 

Is making this math? 

ZZofT " '""J" St3nCe ^ 5665 W ° men as the e-ential 
agents of change in education; but the same women have them- 

atXTuft 3 ° f W ° men ^ 3 n °—** ^-f 

whTtheJ t ^ ^ " d ° Ubly SO " resul < * *at 

when they try to tmplement change they often undo in subtle 

Teachers • 81 

ways with the left hand what they have wrought with the right, 
often undermining their own view of things by their use of such 
language as, "I am just a teacher, but. ..." 

In brief, we are dealing with a situation of uneven develop- 
ment. The problem for society is to give teachers the same pluralist 
support that the best of them give their students. Individuals at 
different places need support to move from where they are. They 
cannot be cajoled or ordered into a too distant place. In my 
writing I hold out the image of an ideal; but even adopting the 
ideal fully is meaningless unless one can see the next small step. 
The practical consequence is that change cannot come about 
except pluralistically. 

The central practical problem is to find ways in which teachers 
who are at different places in the willingness to work for change 
can do so. There cannot be a uniform change across the board- 
any attempt to do that will reduce the pace of change to that of 
the least common denominator. Society cannot afford to keep 
back its potentially best teachers simply because some, or even 
most, are unwilling. 

A Word for Learning 

WW to there no word in E „ g li sh fcr the „ of , 
of SSKIr * e «™ thel 

'^ntag. InlclootTf J " " USSin8 * the parlM »<*« *>< 

'earning. SS^S^" *"."*« ° f *e an of 
fell because there to so 111. , Tt u nameS has not b « n 
■he an of teac^ u " d t L " ^ W ° Uld * *»W 

*e acadende ^t ™^' ^ ^ * 
a" of ieaming to an acad e ™In ,mPO ' ,an, M4 * 
One shouid not be tnisied by the fact that abrades of academic 

A Word for Learning • 83 

departments of psychology often have a section marked "learning 
theory." The older books under this heading deal with the activity 
that is sometimes caricatured by the image of a white-coated 
scientist watching a rat run through a maze; newer volumes are 
more likely to base their theories on the performance of computer 
programs than on the behavior of animals. I do not mean to 
denigrate such books— I am myself the coauthor of one and 
proud of it — but only to observe that they are not about the art 
of learning. They do not, for instance, offer advice to the rat (or the 
computer) about how to learn, though they have much to say to 
the psychologist about how to train a rat. Sometimes they are 
taken as a basis for training children, but I have not been able to 
find in them any useful advice about how to improve my own 

The unequal treatment by our language of the arts of learning 
and of teaching is visible in grammar as well as in vocabulary. 
Think, for example, of parsing the sentence, The teacher teaches 
a child. Teacher is the active subject of the sentence; child is the 
passive object. The teacher does something to the learner. This 
grammatical form bears the stamp of School's hierarchical ideol- 
ogy in representing teaching as the active process. The teacher is 
In control and is therefore the one who needs skill; the learner 
simply has to obey instructions. This asymmetry is so deeply 
rooted that even the advocates of "active" or "constructivist" edu- 
cation find it hard to escape. There are many books and courses 
on the art of constructivist teaching, which talk about the art of 
setting up situations in which the learner will "construct knowl- 
edge"; but I do not know any books on what I would assume to 
be the more difficult art of actually constructing the knowledge. 
The how-to-do-it literature in the constructivist subculture is al- 
most as strongly biased to the teacher side as it is in the instruc- 
tionist subculture. 

A first step toward remedying these deficiencies is to give the 
missing area of study a name so that we can talk about it. Besides, 
" is only respectful to do this: Any culture that shows proper 

84 • The Children's Machine 

respect to the art of learning would have a name for it. In Mind 
storms I proposed a word that did not eateh on, but since I believe 

hat there is more cultural readiness for such a word today I sh J 
try agam-always bearing in mind that my principal goal is 
to advocate this particular word than to emphasize the need 2 
one. If the culture is really ripe for such a word, many people will 
throw m their own words (perhaps simply by quietly using them) 
and event ually one will take root in the soil of the language 
Lmnaeus, the father of botanical terminology, could decide to call 
a fen.har W hi le flower BeUis perennis, but the common language 

,ntT 3 ^ Uti " name aS 11 ^ ores f he botanists 

insistence that a daisy is an "inflorescence" and not a flower at all 
A person can propose; "the culture" or "the language" disposes.' 

n any case, to tllustrate the gap in our language and my pro- 
posal for fillmg it, consider the following sentence: When I learned 

French I acquired knowledge about the language 

— — knowledge about the people, and knowledge 

about learning. Linguistic and cultural would fill in the first two 
blanks with no problems; but the reader will be hard put to think 
up a word to fill in the third blank. My candidate is JatHetic, and 
I hereby make restitution for a semantic theft perpetrated by my 
profes S1 onal ancestors, who stole the word mathematics from a 

dTsoolTT WWdS fe,ated t0 leaming M «««matikos meant 
disposed to learn," mathema was "a lesson," and manthanein 
was the verb "to learn." Mathematicians were so convinced that 
fen was the only true learning that they felt justified in appro- 
notation f 1° ' ******* S ° ^ the dominant con- 
teac • , T m f H ~ " n ° W that StUff about numb - they 

root reL H°h * *** ^ ° f the "«* <*«* 

root retained by current English is "polymath." This isn't a person 

brtad1vT,, many ° f mathematics ' b « one who has learned 
broadly. Following my proposal, I would use the noun mathetics 
for a course on the an of learning, as in: "Mathetics (by whatever 
name « wdl come to be known) is even more important Ln 
mathematics as an area of study for children." 

A Word for Learning • 85 

A comparison with another Greek borrowing for talking about 
mental process will clarify the intended meaning of "mathetics" 
and perhaps support its "sound" and "feel." Heuristics— from the 
same stem as Archimedes' cry "Eureka!" — means the art of intel- 
lectual discovery. In recent times it has been applied specifically 
to discovering solutions of problems. Thus mathetics is to learning 
what heuristics is to problem solving. 

Although the idea of heuristics is old — it goes back at least to 
Descartes and, if one stretches it a little, to the Greeks — its influ- 
ence on contemporary educational thinking is mainly due to 
mathematician George Polya, who is best known through his 
book How to Solve It. His theme runs parallel to my complaint that 
School gives more importance to knowledge about numbers and 
grammar than to knowledge about learning, except that in place 
of the word learning, Polya says "principles of solving problems." 
I would echo this wholeheartedly: In school children are taught 
more about numbers and grammar than about thinking. In an 
early paper (1972) that supported and extended Polya's ideas, I 
even formulated this as a challenging paradox: 

It is usually considered good practice to give people instruction 
in their occupational activities. Now, the occupational activities 
of children are learning, thinking, playing, and the like. Yet, we 
tell them nothing about those things. Instead, we tell them about 
numbers, grammar, and the French Revolution; somehow hop- 
ing that from this disorder the really important things will 
emerge all by themselves. And they sometimes do. But the 
alienation-dropout-drug complex is certainly not less frequent. 
• • . The paradox remains: why don't we teach them to think, to 
learn, to play? 

Traditional education sees intelligence as inherent in the 
human mind and therefore in no need of being learned. This 
would mean that it is proper for School to teach facts, ideas, and 
values on the assumption that human beings (of any age) are 

86 • t,, f r 

Children's Machine 

endowed by nature with the abiJirv m u 
^ed with the simple J^*™*** P ^ challenge 
Probl ems improved when he insZ h ? ^ ^ to *** 
Pie rules as: Before doing an^S **** such sirn . 

to think of other problems ZT Spend * Me time trying 
went on to develop TcTu^on * 0ne * 

W some of wh^hTe^ " heUriStiC " «*» - the 
Problems and some to speX ^ofT' t0 * "»* <* 

Polya himself paid mos^^l ^ ^ whi <* 

Mother ty P i caJ exampteo^r^^ 
Pnneiple of "divide and cona^t ^ ? 
problem because they insist n " ° ften faiJ to solve a 

at once ; in many^e ' n ^ problem 
*ey were to recognize that 1?" h 1" time of * * 

separately and later put together to d ^ P :° b,em Can be so <ved 
^ght Brother hadthe imentSnfiS f ^ t ^ Thus * e 
a Powered airplane that couTd tke^ff f t™'" 8 ° f buiJdi <* 
tned to build such a thing for Z * ^ ^ had ^ 
very likely have come to the ame eXperiments **7 would 
Predecessor I nstead they 0^0^ " ° f 
renting and hum i^tunn ^ u m ° fWin * desi 8" by 
-dons. Then they built that w" ^ X 

toed up with the wind in a p Z e t ^ take ° ff from > track 
Pendently of all this they also worT h ^ Were ideai - '"de- 

i^zr quZ *< : ~ on an en8ine - In this way 

^oiya wished to introdur^ ^ 
«* of the principles of „"? CXpJidt tre at- 

in the same way, I Want JT" ° ften * "problem solving » 
*e Principles of l ean ^g B^ ^ ~ °' 
-Plain the idea of mathetics - n ano^ ab ° Ut h ^ 
™y own unorthodox explan^n o " wh ^ 38 ^ offe »ng 

vas rules. This is not to say that the 

A Word for Learning • 87 

rules are not valuable as aids to solving problems, but I do think 
hat their most important role is less direct and much simpler than 
their literal meaning. Attempting to apply heuristic rules chick! 

2 T: t0 d ° ne Wkh 3 Pf0b,em - d g« on w t 

the next, it has them spend more time with the problems, and my 

mathetic pomt is simply that spending relaxed time with a orob 

lem leads to getting to know it, and through this, to improX 

one* ability to deal with other problems like it. It is not using thf 

fo l^l c 6 P ;° blem; * 18 thinldn8 ab ° Ut the P^blem that 

fostei, learning. So does talking about the problems or showing 

hem to someone else. What is mathetic here is the shift of focuf 

from thinking about whether the rules themselves are effective in 

the immediate application to looking for multiple explanations of 

learnmg. To make the point in a possibly exaggerated form I 
suggest that any kind of "playing with problems" will enhance the 
abilities that lie behind their solution. 

This interpretation of why heuristic methods work highlights 
several mathetically important themes, each of which points fo a 
way in which School impedes learning and to some goodie 
about how to do it better. 

To begin with, the theme of "taking time," just mentioned in 

7nn2T e T" th3n ° nCC ^ CyebrOWS whe * 1 quoted 
osvch f c ^ beSt ' Sd,in8 n****** Traveled, by 
psychiatrist M. Scott Peck. I read the book in the first place for Z 

~ 1 h3V ! ^ and ^do 

correct eveb and politicaity 

con-ect eyebrows to rise at the idea of having any connection with 
people who make money. Anyone who can draw as many people 
«ho situations related to learning as Peck, Lego, or Nintendo 

atte°I S on°Tt in8 th Kl edUCatOTS Wh ° W Boubte holdi "8 the 
attention of thirty children for forty minutes ought to want to 

Here is what Peck has to say about taking time: 

88 • The Children's Machine 

At the age of thirty-seven I learned how to fix things. Prior to that 
tune almost all my attempts to make minor plumbing repairs 
mend toys or assemble boxed furniture according to the accom- 
panying hieroglyphical instruction sheet ended in confusion 
failure and frustration. Despite having managed to make it 
through medical school and support a family as a more or less 
successful executive and psychiatrist, I considered myself to be 
a mechanical idiot. I was convinced I was deficient in some 
gene, or by curse of nature lacking some mystical quality re- 
sponsible for mechanical ability. Then one day at the end of my 
thirty-seventh year, while taking a spring Sunday walk, I hap- 
pened upon a neighbor in the process of repairing a lawn 
mower. After greeting him I remarked, "Boy, I sure admire you 
ve never been able to fix those kind of things or do anything 
hke that My neighbor, without a moment's hesitation, shot 
back, Thats because you don't take the time." I resumed my 
walk, somehow disquieted by the gurulike simplicity, spon- 
tanea and definitiveness of his response. "You don't suppose 
he could be right, do you?" I asked myself. Somehow it regis- 
tered, and the next time the opportunity presented itself to make 
a minor repair I was able to remind myself to take my time The 
parking brake was stuck on a patient's car, and she knew that 
there was something one could do under the dashboard to 
release it, but she didn't know what. I lay down on the floor 
below the front seat of her car. Then I took the time to make 
myself comfortable. Once I was comfortable, I then took the 
time to look at the situation. I looked for several minutes. At first 
all I saw was a confusing jumble of wires and tubes and rods 
whose meaning I did not know. But gradually, in no hurry, I was' 
able to focus my sight on the brake apparatus and trace its 
course. And then it became clear to me that there was a little 
a ch preventing the brake from being released. I slowly studied 
this latch until it became clear to me that if I were to push it 
upward with the tip of my finger it would move easUy and 
would release the brake. And so I did this. One single motion 
one ounce of pressure from a fingertip, and the problem was 
solved. I was a master mechanic! 

Actually, I don't begin to have the knowledge or the time to 

A Word for Learning • 89 

gain that knowledge to be able to fix most mechanical failures, 
given the fact that 1 choose to concentrate my time on non- 
mechanical matters. So I still usually go running to the nearest 
repairman. But I now know that this is a choice I make, and I 
am not cursed or genetically defective or otherwise in- 
capacitated or impotent. And I know that I and anyone else 
who is not mentally defective can solve any problem if we are 
willing to take the time. 

Give yourself time is an absurdly obvious principle that falls 
equally under heuristics and mathetics. Yet School flagrantly con- 
travenes it by its ways of chopping time: "Get out your books 
... do ten problems at the end of chapter 18 . . . DONG . . . there's 
the bell, close the books." Imagine a business executive, or a brain 
surgeon, or a scientist who had to work to such a fragmented 

This story speaks as poignantly about a second theme — talk- 
ing — as about time. Peck does not say this explicitly, but one can 
guess that he would have had the epiphany about taking his time 
at an earlier age than thirty-seven had he talked more often to 
more people about his and their experiences with mechanical 
problems. A central tenet of mathetics is that good discussion 
promotes learning, and one of its central research goals is to 
elucidate the kinds of discussion that do most good and the kinds 
of circumstances that favor such discussions. Yet in most circles 
talking about what really goes on in our minds is blocked by 
taboos as firm as those that inhibited Victorians from expressing 
their sexual fantasies. These taboos are encouraged by School, but 
go far beyond it, and point to ways in which our general culture 
is profoundly "antimathetic." 

An extreme example will vividly illustrate the antimathetic pro- 
cess that exists in many more subtle, but destructive, forms in 
School. The incident took place in a "resource room," where 
children diagnosed as having a learning disability spend part of 
their day. Third-grader Frank was one of them. 

An aide gave Frank a set of sums to do on a piece of paper. I 

90 • THE Chuo Ren . s Machine 

knew the child bi , 

-der other condition! h ^ ^ ^ugh 
number, For example, I had ^ "Zt^ 
lations of how man y and wLTh qU " e im P re ssive calcu- 

** • ** he wanted" to d T To deT^H T ^ * 
calculate with numbers in'isolatn 7 ' ***** demand *> 
number of techniques. One w^T, ^ he had * 

had observed thisand 1,1 J! ^ ^ hiS **** 
^ resource room I could^t^^T ^ aJ, ° Wed * * sat in 
»°ns. But he knew better ^aw 2 ?° f 
^ng else to count with. NothiL t ^ af ° Und for s °™~ 
^trationgrow. What aJdldoS mTw ' 1 C ° Uld « "is 

*e aide to give him something Z do ^ ^ Md persuad * 
But this wouldn't solve any real nr w ^ ^ coun ting. 

back in the same situadonTduclT ? 1 Tomomw he ' d £ 
or Place. Inspiration camel I St ^time 
said out loud: "Did you think 1 Up to th e boy and 

^ his face that he^?^~^ H-ew^y 
^edidn-t. ''^ngisab^nX^ 3ide ' s «** *« 

«m» with a half-concealed^l e 1 *"? t0 ^ He did "is 
subversive idea. ,Je ' ohvio ^ly delighted with the 

In a classic joke, a child stays behinW * 
Personal question. "Teacher "** SCh ° o1 to ** a 

Prised teacher asks, "Why do™, ' ^ t0da y ? " ™e sur- 

"°addy always asks ^ l £fi£** r and *e child replies, 
^at did Frank learn ar/hT ° W What to sa V " 

have said thaThe ^en add * * e -* 

Earned about adding. What wou^d F " t' 0 " Pr ° blemS and so 
^n is that he would be vZ l jkT "* ^ *** tha < * 
about his newly found trick fo7tu r m! f f ° «** f ° his teach er 
abacus. Despite hi 5 fejL* ^ and teeth into an 
Earned not to talk too m^ ab t t w7' * ^ tol * 
J h,s head. He has already^ enctTntl^ ^ ha ^™8 
demanded not only that he get th e Th °° teache « who 

m it in the way they have dec eed ^ bW ^ he 

screed. Le arning to Je{ them ^ 

/l Word for Learning . 91 

that he was doing it their way was part of belonging to the 
culture of School. 8 8 tne 

Franks might be an extreme case, but most people share a 
similar fear of being made vulnerable by exposing themselves as 
having an inferior or messy mind. From this fear grows a habit that 
almost has the force of a taboo against talking freely about how 
we think and most especially about how we learn. If so, my joke 
wxth Frank fits very well with Freud's theory that jokes are funny 
precisely because they aren't-they express repressed feelings 
that are not funny at all, in this case an undertone of something 
wrong with School's way of talking (and especially its way of not 
talking) about learning. Freud was thinking of jokes relieving 
tensions that come from hiding aggressivity and living with taboos 
on sexual instincts. I believe there is a similar situation in relation 
to learning. 

This mathetic taboo has much in common with the taboos that 
existed until recently against talking about sexual matters In Vic- 
torian days, or even when I was a child, sexual fantasies fell under 
the concept of "dirty thoughts," and although it was acceptable to 
recognize that other people had them, respectable people did not 
speak aloud about their own. It is relevant here to speculate about 
what lay behind this reluctance to talk. Imagine that you are a 
Victonan. Now, while you might be pretty sure that you are not 
Oie only one who has dirty thoughts, you would not know just 
how common it is, or whether people would assume you do. So 
better keep your mouth shut. 

Whether or not this is an accurate account of Victorian sex 
taboos, I am sure that something analogous happens nowadays 
Today, few people worry about letting on that their minds are full 
or sexual thoughts; many even feel a taboo against not talking in 
public about this topic. Contemporary taboos bear on different 
aspects of the mind. The most relevant here of many such re- 
straints on intimacy shows itself as a widespread reluctance to 
allow others to see how much confusion pervades one's thinking 

92 • The Children's Machine 

We do no, like to appear ■ ignorant" or "smoin" o, ■ , 
wrong. Of course, we all know ,h» P P 1 * 

™s sy conhasion and ^ Zy^LZ iZ 7 ** * 

we imagine tha, some mind s arc ddy^Tnea a „d sjil H 
no reason to advenise not beinn / ™T topa " dsee 
Presence of people such as „d reached * *° 

over ns. So voices within cantion us " , ££££ whT P °"" 
Talking too much might reveal what ki„!i r ? *" 
make u, vulnerable. LnSv^T J™"" * e have ' Md 

The analogy with S^^^T" * ^ 
reluceance to talk freelv aborc^T , , exa 8Serate the 

own snuggle to achS ^ SZZT^ ' " 
-Pec, has given me a sense o^ ^"1' T "* 
although I have a relariv^h, „ ^ 1 8 ab °°' Even n °w, 

often catch baSe of Actual security, i 

anyone really has. I have devdo^ -an u ^ ^ 1 ^ 

am alone in this— a whole bxtZ Zpa 7 ^ bdieVe *« 1 
shortly be seen. ^ C ' enSe mech anisms , as wilj 

-Piy a matter J^SS * "* ^ ^ " « 
* W of language 

^WnghowIm^^T' P r nB " exam * ^ 
Plate to call a leamm! 7 £f * WhaI ' * * appro' 

^ Word Jbr Learning • 93 

disability and placed in special classes. I was able to read and add 
at the usual age, but there were other areas where my learning fell 
far behind what some children did at my age. Peck reports that he 
discovered when he was thirty-seven that he could, after all deal 
with mechanical problems. It took me a longer time to recover 
from a learning disability that had plagued me as long as I can 
remember: I could not remember the names of flowers. Admit- 
tedly, my agnosia in this domain was not complete. As long as I 
can remember I could correctly apply the words rose, tulip and 
daffodil to the common varieties of these plants. But I cannot 
really say that I knew what a rose was. I was repeatedly in embar- 
rassing situations; when I admired the roses in a garden, they 
would turn out to be camellias or even tulips. I certainly did not 
recognize wild species as roses. The names chrysanthemum, 
dahlia, marigold, and carnation formed a blurry cloud in my 
mind The extent of my not knowing is illustrated by an incident 
that happened well into the transition to "flower literacy" that I 
shall be chronicling in the following pages. 

A pot of plants with rather showy blooms appeared in a com- 
mon space in the building where I have my office. At the time I 
was beginning to pay attention to flowers and was delighted by 
what appeared to me to be a very exotic specimen. When I tried 
to remember whether I had seen one before, the only thought that 
came to mind was that it wasn't a morning glory (a species I had 
discovered" in the previous weeks). As often happens to people 
with learning disabilities, a strong feeling of discomfort inhibited 
me from simply asking the name of the plant. Instead, I tried to 
stnke up conversations about the plant's beauty, hoping that 
someone would mention the name in passing. 

By the time I had failed four or five times, I was engrossed in 
the game of finding the name without actually asking. At this point 
St ° Pped to think > and ca me up with a better ploy than undirected 
conversation. Addressing someone who struck me as the kixid of 
person who would know about flowers, I said: "Isn't that an 
unusual variety?" and success came in the form of: "Oh, I don't 
really know one variety of petunia from another." Petunia! In the 

94 • The Children's Machine 

next few weeks I noticed petunias twenty times before I stopped 
counong. I don't imagine that some person or destiny was plant- 

—re 1 M T" ^ ^ England ' ^ « 

ZTln T PU22lC iS h ° W 1 COU,d have bee " blind to 

them all those years. How was it possible that so many people 

iTidnt WH ^ kn ° Wn ^ 3 ***** lo ° ked i^iS 

1 aian t- what was wrong with me? 

I don't think anything is "wrong with me," but even with all the 

c de" SeCUrfty 1 ^ l ° bui,d °" the ^i S of 

academic successes, I am still vulnerable to doubts about myself 

The pam occasioned by my doubts makes me wonder about the 
eehngs of children who find it so much more difficult than ^ 
comrades to learn to read or to add. Although the consequences 
of my dtsabthty were so much milder than theirs that any compari- 
son „sks bemg condescending, I do think there are enough com- 
mon dements to make the comparison valuable. At the vfry lea* 
my fatlure to benefit from Schoolish remedies gives realn to 

CarefU,ly 3bOUt ***** ~ eS to 

J n ^' S diSC ° UrSe thC idea ° f Nation plays a primary 

2 e th m T r H leam ^ ^ bC ' " ^ ™ 

va e them. The advtce certainly has no direct application to my 

case for ,n every simple sense of the word I was already highly 

monvatedl often made resolutions to conquer my flowed 

abddy, and these would lead to a spun of intense flower na m _ 

learmng activity. For the same reason, laziness is no exp anation 

either. We have to look more deeply for much more subtle and 

textured nottons for thinking about these disabilities and str te 

«r 0 r:i conc H ept of ; being motivated -" 1 ^ * ~ 

cept of relatronshtp with areas of knowledge having all the 
complexity and nuance of relationships with people 8 

iJ I would f hT ?* d6SPite a " my fenCy ideas about 'earn- 
nl .1 T t ^ °" SCh ° 0liSh m ° des of '^"ing flower 

names. Lookmg for a teacher, I'd go into a flower shop and ask- 

A Word for Learning • 95 

What are those? And those? And those? Looking for a textbook, I 
bought a book from which I tried to associate photographs of 
flowers with their names. I even went on field trips to the botani- 
cal gardens where I would peer at the name tags of all the flowers. 
But to no avail. The frontal attack by rote learning didn't work any 
better for me than the same Schoolish methods do for children 
who have trouble learning School's subjects. It was like learning 
for a school test. I'd remember the names of a few flowers for a 
while, but they would soon sink back into the familiar confusion. 
After a while the paroxysm of flower learning would pass, and I'd 
resign myself for another year or two to being someone who "isn't 
good at" flower names. 

One day a break came serendipitously. I was in the country in 
the late spring among people who were talking about how won- 
derful the lupines were doing. Feeling excluded and not wanting 
to admit in that particular company that I had no idea what a 
lupine was, I used the trick that later served me well in the petunia 
situation. I said: "Isn't Loo Pin a strange name? I wonder what its 
origin could possibly be?" (Getting a conversation going is a good 
ploy used cunningly by many "learning-disabled" children.) 
Someone speculated intelligently: "Sounds like Wolf—lupus the 
wolf. But I don't see the connection." After a few rounds of 
comment in scattered directions (which would have died out if I 
hadn't kept stoking the conversational fire), someone said: "It 
looks like a wolf's tail." Someone grumbled that it didn't really. 
That's a relative judgment, for what mattered to me was that of all 
the plants in sight, only one could possibly be perceived as being 
in the slightest like a wolfs tail. So I concluded, correctly, that 
those colorful masses of what I have since learned to describe as 
"tall spikes" were lupines. 

The aspect of the serendipity that played a key role in my 
development wasn't discovering what those flowers were called; 
it wasn't making a connection between a flower and a name. It 
was making a connection between two areas of knowledge: 
flower names and a particular kind of interest I happen to have in 

96 • The Children's Machine 

etymology. Previous experience leads me to expect that I would 
soon have forgotten the name lupine, but this time I was so 

Z f^t™ . my ; ,CVemess and in <rigued ^ the etymological puz- 
zle that the incident was still buzzing in my head when I got back 
o m y b oks a n d couId explore the word. I read that lupfne does 
ndeed denve from the ^ WQrd fof ^ ^ ^ f^J* 

he tail-like appearance of its spike. The word is traced to a belief 
that lupines were bad for the soil because they "wolfed" all the 
nutnents. Enjoyment of the wolf-theory's ambiguous status be- 

TZtT 6 fa,se J ed me to pureue the ~ h - ™ 

a twist in the story that made it still more evocative for me 

As long as I can remember, I have been excited by paradoxical 
aspects of words, and so my level of excitement rose IL I found 
a paradoxical slant to the etymology of lupine. One no longer 
thinks of the lupine as wolfing nutrients; on the contrary the 

from the atmosphere and add value to the soil. Seeing them in 
poor sod is cause for praise rather £han 

outlived the theory on which it was based, and so became o„e"f 
many examples of old ideas that are preserved in our language 
and maintain connections of which we are only marginally awaT 
My ^relationship with flower names was taking^ a new'ton^ 
they made contact with areas I found personally interesting. 

This twist also touched on another personally evocative issue. 
One reason for my fondness for etymology is that it provides 
good examples for a vendetta against the idea of any sinlS 

nted ° n °w T ntal Phen0mena ' ^ « " -lU deter- 
Now thTo 15 fn^ 6SSenCe ° f thC W3y «* -n" "works, 
rata tut 7 3T ei bC8an to show P romise - an 

wl of Str ° ng ^ VCiy ^ SU PP° rt for ^ 

counte r 8 ' f ' ** ^ seem to run 

oft'Teems? ? ^ ** ex P la ^ons, since it so 

often seems to pinpoint a single historical source for a word But 

the w 8 T UfCe i S 3 P ^ cholo 8 ical <* cultural explanation of 
the way the word is used. The wolfing-of-goodness theory may 

A Word for Learning • 97 

i be at the root of a full explanation of old popular forms that 
I seem to have been followed by Linnaeus when he called this 
I genus of plants Lupinus, but it scarcely begins to be an explana- 
I tion of why the name has stuck in our culture. Explaining why 
I botanists call a plant what they do does not explain why plain 
folk do so — in most cases the popular language scorns the bo- 
1 tanical name and develops its own. We say lilac rather than 
1 syringa and wear a carnation rather than a dianthus in a 
H buttonhole. It seems plausible that a folk etymology such as the 
| looks-like-a-wolf's-tail theory could have contributed together 
I with the wolfing-the-goodness theory to making the name lu- 
pine stick in popular usage. After all, if the association occurred 
. to one person, it is reasonable to assume that it occurred to 
1 others and that it hovers near the threshold of consciousness of 
1 many more. 

| My mathetic theory does not depend on the truth of my ama- 
!;'teur etymologizing. What matters here is that it was connected 
| with regions of knowledge that were strongly evocative for me. 
JfThe real moral of the story is how a certain engaging quality 
i spread from words to flowers, and later from flowers to other 
O mental domains. If I had to sum it up in a single metaphor, I would 
say it is about how "cold" mental regions were heated up through 
contact with "hot" regions. 
||| One contact was not enough to heat up the previously chilly 
gpgion of flower names. By now, as I write two years after the 
ilupine incident, there has been dramatic change in my memory for 
j§Ower names. It is as if they now find a place to stick. But this did 
not happen all at once, and by the time it did, much more than the 
ability to remember their names had changed in my relationship 
with plants. 

M For most of a year there was not much change, although I did 
J|pt forget the word lupine and I did notice myself paying atcen- 
|PQn to oddities in flower names. For example, I caught myself 
laying with the minor contradictions suggested by an etymologi- 
literal-minded hearing of "white lilac" or "yellow rose." Li-lac 

98 * THE C »aD R EN- s Machine 

** same kind of oddness Z ^ZT t «"* ° ne ' S ear «° -"se 
to aren't (in a botanical sense) ji^^ T' ^ ^ ^ 

they kept making sma« ripple 7^ T ^ 
l am glad because these ripZfl 1 " ""^ ^ in 

grand whammer. On *2 f *T 3 *»* ° f rea ^ess for 
™ ng)IranheadJ e at about two in the 
not a flower. 8 ° the hct that for a botanist a daisy is 

I can't telJ whether r 
having , ive d J ^^Z^^"*******, 
Come on. It's the prot^ a flow™" 8 5 A ** » *»J 
year to draw a flower, ,w d h ^ had 3Sked ™ last 

rather i 8norant> , reaJ1 ^ ^ ^™° U S h * s% now> and 
in the small houL, C^i"" ^ book to 
putsch against standard nc^eneT ^ " eWS Was 

•"elude sunflowers and blacken beyond **** to 

and dahlias. They were Z^T" «* ^anthemums 
or elevated with fancy name Tk e "fl ^ " hke flo — 

^at in man y circles 7is a dennt Z?™**™*' " b « it appeared 
-n this be? A sunflower J^ff* them fl —s. How 
already been slighted in ^ J^TT™^^** 
excluded from being flowers Y * ^ Mes ' ^ now 

The most powerful m 
could at last get hold of ToTflowTV? m0min8 whe " ' 
»°n that would be ^^^J^^^J"^^ a situa- 
I was looking at a familiar ob,S wl * f ° ,,OWin S year: 
* e fi ™ time. Compare a bXJn wT" * ***** at » *>' 
bf " to understand how the bo^. T * *** you ™y 
tally different things. For Z bT *** them 3S ^men 
around its sex organs: The stme n ?h ' " Struct -d 

tnas, and ovaries are the es^Tce oAh 7^' the pistiJs ' s tig- 
•** that make such a ^^^T' -tals Jd 

y COJo rhil impression on us 

A Word for Learning • 99 

The family of flowers that includes daisies, asters, sunflowers and 
coneflowers are called inflorescences because what we usually call 
a flower is seen by the botanist as a mass of tiny flowers. 

and on the birds and insects are secondary features. In the but- 
tercup, the tulip, and the lily you can see all these parts— but 
not in the daisy. Or rather, in the daisy you see the pans re- 
peated many times, for those white slivers you may have pulled 
off one by one while reciting "loves me . . . loves me not . . ." 
are not petals surrounding sex organs but entire flowers. If you 
pull one out very carefully, you will see that it is like a miniature, 
lopsided, and elongated petunia. And what they surround, the 
central yellow disk, is itself a mass of even tinier complete flow- 
ers. So botanically speaking, the daisy is not a flower but a tight 
bunch of flowers of two kinds, ray flowers on the outside sur- 
rounding disk flowers on the inside. The botanist will call it a 
head or an inflorescence, though I suppose and hope that chil- 
dren will always call it a flower. 

100 • The Children's Machine 

The disk or mass at the center of many inflorescences is made up 
of many tmy flowers like this one. What seem to be petals are also 
complete flowers in themselves. 

Up to this point my new involvement with flowers was con- 
fined to their names and belonged squarely in my established area 
of hot interest in etymology. With the daisy incident it broke out 
from words to things. I began to look at flowers and think about 
their structure. The concept of flower was changing, and new 
conceptual entities began to grow in my mind: The unit of thought 
shifted from the flower to the whole plant, and, by degrees, previ- 
ously nebulous entities such as "the rose family" (which includes 
chernes, apples, and strawberries as well as roses) acquired firmer 
reality. I also began to think about botanists: It was easy to see that 
their definition of flower excluded daisies; this was a simple matter 
of logic. But coming to appreciate the reasons for adopting such 
a definition was an essentially different and more complex pro- 
cess, better characterized as entering a culture than as understand- 
ing a concept. 

Naming remained an important theme in an increasingly com- 
plex set of relationships in my mind. A simple example started 

A Word far Learning • 101 

with the name of the daisy. Now that the humble flower had 
become such a center of interest, I naturally poked around the 
origins and meanings of its name. I could hardly believe my luck: 
daisy is "day's eye"! What a find, accompanied again by amaze- 
ment at not having known this and even some shamefaced puz- 
zling about why it hadn't been obvious. The find got extra spice 
from the fact that different books gave different explanations. One 
theory had the daisy looking like the sun, which is the "eye of the 
day"; another associated it with the tendency of daisies to open in 
the day and close at night. Another started with a speculation. I 
had run into the fact that daisies were thought to have good 
medicinal properties for afflictions of the eye. A first guess that this 
might be related to its name seemed to me too implausible to be 
worth checking. Doing so all the same led to another curious find: 
the doctrine of signatures, which held that plants show by their 
visible properties their medicinal virtues. The self-heal, a wild- 
flower, shows its value for treating throat ailments by the fact that 
its flower has a throat, and this is reflected in the derivation of its 
botanical name, Prunella vulgaris, from Breune, the German 
word for "quinsy" (an old-fashioned name, as I learned through 
the same investigation, for tonsillitis). The coloration patterns 
of hepatica leaves are said to suggest the appearance of the liver, 
thus explaining both the name hepatica — from the Latin word 
meaning "having to do with the liver" — and the belief that it is 
good for liver ailments. Certain features of plants became more 
salient, for example, that some have throats and some don't. 
The interest in names was bringing me into the real world of 

Other connections with names and naming led into new rela- 
tionships with nature. The window of the room where most of 
this book was written looks out on a field in which I see wild- 
flowers of several colors, particularly yellows and purples. 
Among the yellows I can see tall, bushy Saint-John's-worts and 
even taller evening primroses, little cinquefoils, and some early 
goldenrod. Among the purples I see fireweed, loosestrife, and 

102 • The Children's Machine 

asters. I also see some that are question marks in my head- T 
have noted their existence but don't know what they are tto 

ir^ir u / diff r tiated disp,ay 

nol Trl ' u "• BUt * W3S n0t at a]1 what I ^ seeing 
as I did before. I cannot imagine what it would be like to see 

^:i^ flowers as a — - *~ jslt* 

procIsToH PUrSUC l dCtail ^ thiS deVel °P me «t as a model for the 

conel ^ 8 - ^° ^ 380 1 ^ the " ame and 

w^delJ 1 w P ^ t0 COmm ° n bUtterCUpS - 1 cannot ^ how 

"mt e Z TH 7 USed l thiS namC t0 apply f ° 0ther s P-es, but 
am sure that I had no other words for small yellow flowers Early 

rn ^e first summer I became aware of two other kinds of yellow 

wtldflowers: anquefoils and Saint-John's-worts. But my degree of 

flower dyslexia showed itself in the fact that I had to X? 

these flowers many times-like someone who canncThnW 

tune,lcould not hold the ^^^^1 

*™Z7rT 8 h : d happened: !t - » « -"e ^ 

ZZl ^ ZT n8S - buttercu P*. anquefoils, and Saint- 
it r hT , Ut yet kn ° W What to ha "8 on each pee or 

£^3r ^ p,e and had been tow ~ u 

and am struck by how I get new entities mixed up until a gradually 
f h r™ l**^ b — s strongloug^etp 

si :/;— lty 8rew siow,y and - 

hapcted 1 ButTn * h ™ *is process of growth 

3 1 J d ° kn ° W h ° W * did not ^PPen: I tried to 

tese Z e e t 7 * 1 had been -Crested on y in 

tZu^ WerS ' W ° Uld h3Ve bCen aWe to memorize their 

r// tum r d to ° ther «— - d -» 

something Hiff ' 1 WOuld « et il wr °ng again. Slowly 

somethmg different from rote memory of botanists' defining char- 

A Word for Learning • 103 

acteristics developed; I began to build up a more personal kind of 

I associate buttercups with folklore that tells about the appear- 
ance of a person's chin when a buttercup is held up to it. If the 
chin takes on the yellow color by reflection, this is interpreted in 
America as a sign of liking butter and in France, naturally, as a sign 
of being in love. Through these stories I associate the buttercup 
with shiny petals, one of the characteristics that in fact distin- 
guishes it from the other two. Other associations were less direct. 
One of the three flowers has especially bushy stamens. I couldn't 
remember which. In fact, it is the Saint-John's-wort, but when I 
read that this plant is also known as Aaron's beard, I associated 
this name with bushy stamens because these are like a beard, and 
with the name Saint-John's-wort because Aaron and St. John both 
have a biblical connection. So the name Aaron's beard acted as a 
kind of glue to stick the bushy stamen property to the name 
Saint-John 's-wort. During the same period I found my visual at- 
tention shifting from the flower to the plant, and this brought new 
kinds of association. And so it went. 

The deeper I got into my "affair" with flowers, the more con- 
nections were made; and more connections meant that I was 
drawn in all the more strongly, that the new connections sup- 
ported one another more effectively, and that they were more and 
more likely to be long-lasting. Moreover, the content of my learn- 
ing spread in many directions: I was learning Latin words, I was 
picking up insights into the history of folk-medicine, and I was 
gaining or renewing geographic and historical knowledge. The 
Renaissance in its artistic and scientific aspects came into new 
focus through the role of flowers in the new relationship with 
nature that developed at that time. 

My learning had hit a critical level, in the sense of the critical- 
mass phenomenon of a nuclear reaction or the explosion of a 
population when conditions favor both birthrate and survival. The 
Pimple moral is that learning explodes when you stay with it: A 
ftxll year had passed before the effect in my mind reached a critical 

104 • The Children's Machine 

level for an exponential explosion of growth. The more complex 
moral is that some domains of knowledge, such as plants, are 
especially rich in connections and particularly prone to give rise to 
explosions of learning. 

My learning experience with flowers began with a very narrow 
"curriculum": learning to name them. In the end the experience 
widened and left me a different person in more dimensions of life 
than anything that is measured by the standardized behavioristic 
tests with which the conservatives judge School learning. It af- 
fected my stream of consciousness as I moved about the world: I 
see more as I walk in the street or in a field. The world is more 
beautiful. My sense of oneness with nature is stronger. My caring 
about environmental issues is deep and more personal. And re- 
cently I have surprised myself by enjoying systematic books on 
botany and having no trouble remembering what I read. It is as if 
I have made my transition in this domain from a concrete to a 
formal stage. 

Early in this chapter I mentioned a mathetic weakness in the 
literature on constructivism. The metaphor of learning by con- 
structing one's own knowledge has great rhetorical power against 
the image of knowledge transmitted though a pipeline from 
teacher to student. But it is only a metaphor, and reflection on my 
flower story consolidates my sense that other images are just as 
useful for understanding learning, and are more useful as sources 
of practical mathetic guidance. One of these is cultivation: Devel- 
oping my knowledge of plants felt more like the work of a hor- 
ticulturalist designing, planting, and tending a garden than the 
work of a construction crew putting up a house. I have no doubt 
that my knowledge developed even when I was not paying atten- 
tion! Another image is the geographic metaphor of regions and the 
idea of connections between them. Indeed, the description "con- 
nectionism" fits my story better than "constructivism." 

On a pragmatic level, "Look for connections!" is sound math- 
etic advice, and on a theoretical level the metaphor leads to a 

A Word for Learning • 105 

range of interesting questions about the connectivity of knowl- 
edge. It even suggests that the deliberate part of learning consists 
of making connections between mental entities that already exist; 
new mental entities seem to come into existence in more subtle 
ways that escape conscious control. However that may be, think- 
ing about the interconnectivity of knowledge suggests a theory of 
why some knowledge is so easily acquired without deliberate 
teaching. In the sense in which it is said that no two Americans are 
separated by more than five handshakes, this cultural knowledge 
is so interconnected that learning will spread by free migration to 
all its regions. This suggests a strategy to facilitate learning by 
improving the connectivity in the learning environment, by ac- 
tions on cultures rather than on individuals. 


An Anthology of 
Learning Stories 

THE word anthology will do to capture a key point about 
mathetics: the richness of connectivity of the things we 
know. In my case, the etymology of lupine led to new 
relationships with flowers, which in turn led me to acquire several 
hundred entirely new words and "heated up" my awareness of 
thousands of old friends. I must have known the word anther (the 
pollen sac of a flower's stamen), and its Greek stem anthos, mean- 
ing flower, from my school days. But I knew them "coldly " When 
they heated up they stirred connections, and I began to wonder 
whether anthology had an ancestral meaning of "studying flow- 
ers." This, however, turned out to be a false analogy with words 
like biology. Actually, the suffix -logy has a more general etymolog- 
ical sense than "study of." Its Greek (and Indo-European) stem 
meant "collect" before it meant "study," which could be regarded 
as collecting knowledge. Etymologically, anthology is a collection 
or bunch of flowers. Think of trilogy, which is not the study of 
threeness but a collection of three things. 

This chapter is a collection of learning stories, each of which is 
prefaced and postfaced with just some of the learning morals that 

An Anthology of Learning Stories • 107 

can be taken from it. The stories deal alternately with children 
using technology in a school and with people in the "real world." 

Debbie Learns Fractions 

In my discussion of my relationship with plants I suggested two 
modes of learning. Propositions cleanly state a well-delimited fact, 
such as "Potentilla is a genus in the rose family." Explorations 
establish a relatively messy web of connections which may link 
potentillas with buttercups and oenethera and etymologies and 
cabbages and kings. I probably gave the impression of strongly 
favoring the messy web over the clean proposition. I would stand 
by this insofar as the web can include the proposition, but the 
propositional does not include the web. Ideally, one should be 
able to draw on both and move fluently between them. But I 
should much rather have a messy intuitive understanding of 
something that I have not been able to formulate in a crisp propo- 
sition than have a crisp, clean proposition without an intuition to 
back it. Unfortunately, School's preference for the testable, delimi- 
table, and listable proposition reverses this order. The result is 
isolated pieces of "knowledge" without the intuitions and the 
connections that would justify taking off those quote marks. 

For three months Debbie and the other members of her fourth- 
grade class were engaged for an hour a day in a project that turned 
the tables on the use of the computer for automated instruction, 
generally known as CAI. Here the fourth-graders had the assign- 
ment of using Logo to develop a piece of instructional software to 
teach something about fractions; they became producers instead 
of consumers of educational software. To the true believer in CAI, 
this reversal will seem as perverse as telling people who need to 
move from point A to point B that they should build cars instead 
of using them. But the fact is that making the software did turn out 
to favor learning about fractions — as well, of course, as learning 

108 • The Children's Machine 

Logo programming and other skills specifically related to making 
software. (I would not deduce that the same reversal applies to 
building cars, though it is far from impossible that building one 
might make a person a better driver!) 

The paradox in the reversal is especially marked in the case of 
Debbie. The students were free to choose what they wanted their 
software to explain about fractions. Some of them chose to ex- 
plain how to do the kinds of manipulation that come up in school 
tests — such as converting two-fourths to one-half. Debbie was 
one of those whose test scores showed significant improvement 
even though what she chose to explain was something more 
philosophical and far removed from any of the skills on which she 
would be tested. She formulated her philosophical principle in a 
number of ways, including, "You can use fractions every day of 
your life," and, "You can put fractions on everything." What she 
meant by these statements will become apparent from the context 
of her work. 

In an interview early in the research project (which formed the 
core of a Ph.D. dissertation by my colleague and former student 
Idit Harel), the children were asked the simple question, "What's 
a fraction?" Their answers to this question were even more disqui- 
eting than their low test scores. Some seemed unable to give any 
sort of answer beyond an example, which was usually "a half." 
One said, "We haven't done that yet," evidently meaning not that 
they hadn't "done" fractions in class— of which, so far as these 
children were concerned, they had done plenty— but that they 
hadn't yet been told how to define a fraction. Many gave an 
answer that could be considered, taken in itself, quite reasonable 
for a fourth-grader: "A fraction is a part, it's a part of something." 
What was worrying about this answer emerged when the investi- 
gator asked for examples of fractions. Almost all the examples 
given were of just one kind: a physical piece of a physical thing 
such as a slice of a pie. What is wrong with that is seen by 
comparing it with what the same children said four months later. 
After their experience as software designers, their examples be- 

An Anthology of Learning Stories • 109 

came enormously varied: half an hour, twenty-five cents, a half- 
price sale, daytime. Debbie topped the variety of examples by her 
general principle, which came down to saying: "Why are you 
bothering me to give specific examples of fractions? . . . Don't you 
see that anything you think of can be an example of a fraction?" 

Debbie's theory of fractions, which is quite remarkable in itself, 
is even more striking when contrasted with her position in the 
initial interview. When asked to show an example of a fraction, 
she drew a circle, divided it in two, shaded in the right half, and 
said, "There: that's a fraction; that's a half." When the investigator 
asked her about the unshaded side, she said, "No, that's not a 
fraction; that's nothing." For Debbie a "fraction" was not only a 
part of a physical thing, it was a shaded part of a circle. Moreover, 
it had to be shaded on the right side. The investigator, noticing 
that Debbie presented all her examples in this orientation, rotated 
one of her drawings so that the shaded side was up. Was that a 
fraction? Debbie's answer at least showed that she was thinking 
and not simply answering mindlessly: "Kind of," she said, "you 
can turn it"; and she rotated it back to the preferred position so 
that it now became a "fraction." 

The point here is not that these restricted answers represented 
Debbie's total knowledge about fractions. She probably would 
have acquitted herself well enough in a squabble with a sibling 
about the distribution of candy. The point is that formal school 
knowledge of fractions was not connected with her intuitive 
everyday knowledge. What she learned in class was brittle, formal, 
and isolated from life. Attempts by teachers and textbook authors 
to connect school fractions with real life via representations as pies 
simply resulted in a new rigidity. Her participation in this project, 
on the other hand, led to more living connections. The shift in 
Debbie's thinking was not just a matter of knowing facts and skills. 
Her phrase "you can put them on top of anything" showed an 
epistemological shift and an epistemological intention. She made 
a shift from one kind of knowledge (formal, teacher's knowledge) 
to another kind (personal, concrete, her own). At the beginning, 

110 • The Children's Machine 

a "fraction" was a definite thing about which she had learned from 
a teacher. At the end, "fractions" meant a way of looking at the 
world. "Putting fractions on" something meant using them as a 
way of thinking about, a particular view of, whatever you put 
them on. 

The way the shift actually happened was like this. Debbie had 
been trying to draw fractions on the computer screen. At first this 
was easy: A fraction was a divided and partly shaded circle, so she 
had simply to master the means needed to create such figures on 
the screen, as shown in the illustration on the page opposite. 

An awakening new interest led her to want more varied exam- 
ples, and eventually to her announcing her discovery in the de- 
signer's notebook that each of the students was asked to keep. The 
illustration of a page from the notebook on page 112 shows her 
excitement in writing it and the importance she attached to the 

What made the shift happen? What led to the awakening of the 
new interest? 

A full discussion would have to treat many aspects of a complex 
situation. Among these, I believe that an essential aspect was the 
quality of feeling "serious"— as with my newspaper and Piaget's 
schoolboy articles, or the assertion of national, professional, and 
gender pride by the Costa Rican teachers, Debbie's project moved 
out of the category of assignment to be gotten out of the way as 
soon as possible. Instead, it became a personally meaningful un- 
dertaking capable of mobilizing intellectual energy. Other inter- 
pretations are discussed in Harel's book, Children as Software 
Designers, which offers the most thorough discussion I have seen 
of a single experiment on children using computers. 

Debbie's software design project did not have this quality of 
engagement from the beginning. During the first few weeks she 
gave it only the most desultory attention, sharing her time at the 
computer between somewhat listless dabbling with drawing some 
representations of fractions on the screen and much more ener- 
gized concentration on putting up animated decorations for 
poems she had written about her personal feelings. One day, 

An Anthology of Learning Stories • 111 


All of these ah*p«» 1/2! 

Debbie uses this screen to convey her discovery about fractions: 
Fractions are everywhere. 

serendipity made a connection between the two activities. She 
realized that a programming technique she was using for her 
decorations could be used to make her representations of a frac- 
tion more visually interesting. One thing led to another. A class- 
mate noticed her screen and asked how she got that effect. Sud- 
denly this girl who had led an undistinguished life as a class 
member found herself in demand as an "expert" who had knowl- 
edge that others wanted. Her attitude to the software design proj- 
ect changed. Previously she had wanted to stay out of it as far as 
she could; now, basking in her success, she wanted to be in it as 
j&r as she could. So she started exploring, looking for fractions. 

Debbie's project now started taking her "among the fractions" 
[|l the real world around her, giving them an existence for her they 
had never had before. Previously, fractions had existed only in the 
classroom, and even within those narrow confines they were 
Anther restricted to the teacher's blackboard and to Debbie's 
[Worksheets. There was no toehold for her to explore them, to 

An Anthology of Learning Stories • 113 

engage with them. When she left the classroom she left them 
behind. No wonder she saw them nowhere except in the pie 
diagrams through which they were presented to her in class. Now 
Debbie the poet gradually began to see fractions everywhere. She 
was on her way to building a new relationship with fractions by 
allowing them into her web of real interests in defiance of School's 
balkanized rules: Poetry is poetry and math is math. 

Kitchen Math 

A recent "discovery" by ethnographers showed that women en- 
gaged in household tasks know and use more mathematics than 
one would suspect from Schoolish tests, only they know it in 
forms different from what School teaches. The cognitive an- 
thropologist Jean Lave observed how women working in their 
kitchens adapted recipes to adjust the total quantity. From a 
Schoolish point of view this appears to be a problem in fractions 
(or "proportions"), but the women did not use the numerical 
methods they had been taught in School. Instead, they employed 
ad hoc "concrete" methods based on the specific situation. The 
results of this piece of formal research resonate with my own 
informal experiences (and no doubt with those of many readers). 

I was momentarily shocked when a friend with whom I was 
cooking computed two-thirds of one-and-a-half cups of flour by 
the following procedure: Measure one-and-a-half cups onto the 
pastry board, spread it into a circle, divide the circle into thiree 
slices by making a symmetrical pie-cut pattern, and put one slice 
back into the flour canister. My mind "sees" one-and-a-half as 
ithree pieces (each equal to one-half) so directly that I needed time 
to empathize with the problem. 1 was helped to put this in per- 
spective when another friend who read a draft of this text pointed 
out that she directly "sees" the identity of plants, whereas I go 
ihrough an analytic cycle of noting leaf forms and flower scruc- 

114 • The Children's Machine 

tures. Still, even though she had read my account and made an 
intelligent comment, she had not "seen" what I "saw," since she 
went on to offer another solution to the flour problem that took 
my mathematician's breath away both for what she "saw" and for 
what she did not "see." She said, hesitating and presumably think- 
ing as she went along, but with a strong voice that expressed 
confidence: "I would use the one-third-cup measure . . . every 
kitchen has one . . . you can use it twice to get two-thirds of a cup 
. . . and then . . , well ... if you use it once you'll get two-thirds 
of half a cup ... so that gives you two-thirds of a cup and 
two-thirds of half a cup." Her thought process is illustrated on the 
page opposite. 

In my mathematician's language I redescribed this to myself as 
a deduction: two-thirds of half a cup equals half of two-thirds of 
a cup, equals one-third of a cup. But when I asked my friend to 
explain why her plan would work, she found no such words. The 
math reticence inherited from School many years before re- 
asserted itself and she started off with: "Oh . . . One-and-a-half 
. . . that's five-thirds . . . isn't it'" and faded away into a little voice. 
The shift in voice spoke volumes. The strong voice and the com- 
petent kitchen math said she was in her territory; the little fading 
voice and the incompetent excursion into School math said she 
was in a territory which was "the other person's," as well as being 
especially alienating for her. 

Two aspects of this, epistemological and mathetic, are impor- 
tant, and of course the relationship between them. Kitchen math 
highlights the futility of School math from a point of view that goes 
beyond the critique of School's ways of trying to convey knowl- 
edge. What is called in question here is the knowledge itself: Not 
only does School use faulty methods of teaching, what it teaches 
is not what people use when they have to deal with a real prob- 
lem. None of us, including myself, used the abstract, formal 
school-math approach which would be to convert 1 VS to *h, then 
do something like: 

An Anthology of Learning Stories -115 

A representation of what might have been going on in the head of 
someone doing kitchen math. 

) The central epistemological moral is that we all used concrete 
forms of reasoning. The central mathetic moral is that in doing this 
3we demonstrated we had learned to do something mathematical 
svithout instruction— and even despite having been taught to 
proceed differently. 

I This widespread use of mathematical methods that were not 

116 • The Children's Machine 

taught is not grounds for educational complacency. People are 
still limited in what they can do. The conclusion to be drawn is not 
that they do it anyway and so do not need help, but that what they 
learn informally points to a form of knowing and learning that 
seems to come naturally to people but goes against the grain of 
School. The question for educators is whether we can join it 
instead of fighting it. To do this we need to know more about 
what "it" is. What kind of learning lies behind kitchen math 
knowledge, and how can we foster and extend it? 
Could we make kitchen math part of School? 
It would miss the point entirely if this were done by dressing 
up the old School exercises in kitchen clothing. What made the 
kitchen math work was not that it "felt relevant" because it was 
"about flour." It worked because the mathematical action was 
not separate from the rest of the work of baking. It was an ex- 
tension of the familiar, syntonic actions of manipulating the in- 
struments and substances of the kitchen. One could indeed 
make kitchen math part of School by making School part of the 

Another way is to recognize the ways in which Debbie was 
doing something like kitchen math. The computer became 
her kitchen for writing and decorating her poems, and then she 
could do the work on fractions as a seamless continuation of 

Maria Builds a House 

Debbie's story, and the one about the flour, revolve around peo- 
ple's sense of connection and disconnection with mathematics. In 
contemporary society another, ultimately more noxious, issue of 
disconnection dominates most people's relationship with technol- 
ogy. The chapter on teachers mentioned examples of the relation- 
ship being improved. The adoption of the computer as an exten- 
sion of a personal style of teaching allowed something like the 

An Anthology of Learning Stories • 117 

seamless continuation of the kitchen math. My next story allows 
a child to use a familiar toy as her kitchen. 

"Will we really play with that? Here in school?" a fourth-grader 
exclaimed gleefully as he came into a room in which there was 
more Lego material than he had ever seen in one place. Francisco's 
initial surprise at meeting this kind of stuff in school was soon to 
be exceeded by greater surprises at how it was different from what 
he had at home. In addition to the familiar plastic building bricks, 
there were gears and motors whose uses he understood immedi- 
ately, there were some more mysterious objects called "sensors," 
and, most remarkably, a way to connect the motors and sensors 
to a computer. He was told that with sensors he would make Lego 
models that could see and feel. He didn't quite believe that but 
was sure that he was going to have a great time. 

Maria*, Francisco's classmate, had a more complex reaction. 
The pleasure of anticipating that whatever was going to happen 
would at least be a change from the usual class scheduled for this 
period was tinged with some apprehension. Sure enough, her 
initial feeling that this was boys' stuff was soon reinforced as the 
teacher, who didn't appear quite comfortable with it herself, 
showed a truck built by another class. The truck could be started 
;and stopped or reversed by typing at a computer. The teacher 
talked most excitedly about how the truck would go into reverse 
by itself if it hit an obstacle. "You will soon all be able to build 
something like that and then you will understand how a lot of 
things work." Maria felt a familiar tightening in her stomach. Al- 
though she would have liked to understand how a lot of things 
worked, she really couldn't see herself building trucks with any 
enthusiasm. When she heard that the class would do this for two 
double periods twice a week for six weeks, her conflict turned to 

*Maria is an interpretive composite of several students. However, I am firmly 
convinced that any one of them could have acted and thought as I present her. 

118 • The Children's Machine 

By the next week the Marias and Franciscos in the class were 
coping with what they learned to call the Lego-Logo workshop by 
creating a fourth-grade version of the "two cultures" image made 
famous by C. P. Snow. Francisco had picked up the idea of build- 
ing a truck and went on to invent an automatic shift mechanism 
to put his vehicle into low gear when it had to climb a steep slope 
Others like him had left the idea of a truck to build robots, fantas- 
tic animals," and other constructions that moved, shook spun 
and made a lot of noise. P ' 

On the other side of the cultural divide Maria and three of her 
friends were doing something quite different. Greatly relieved to 
find that they were not forced to make trucks, they were building 
a house. They were not trying to invent a machine that would "do 
something." They were making something that felt familiar and 
was going to "be beautiful." 

In this they continued what they had done with Lego when 
they had played with it at home as preschoolers, before their 
growing sophistication outpaced their limited supply of materials 
Here the greater supply of Lego parts gave them a chance to do 

more STr^f T*"** *»* °" * ^ be " er > and 

more beautiful ^ Apart from sheer q{ ^ 

did not take advantage of any special features of this Lego setup 
they made no use of motors, sensors, or connections to the com- 
puter. The cultural division was dramatic and quite familiar Tech- 
nology versus art, science versus the humanities. Those of us who 
were aware of these issues watched, intrigued. How would these 

W 1 ^ iff " Pr ° blem that C R W had found insupera- 
ble? Would they accept the divide? Could they bridge it? Would 
they want to do so? 

It took time, but in the end Maria and her friends found their 
own way to cross the culture gap. Their manner of doing so is rich 
with insights into how the divide is rooted in our cultures and our 
schools, how it is linked with other divisions of style, gender, and 
ethnic ways, and how it can be crossed 

During the first week Maria's group learned how to exploit 

An Anthology of learning Stories • 119 

the divide. Each child brought to the group's pool a ration of 
Lego parts. Since trade with other groups was permitted for 
greater flexibility in individual projects, a bartering market devel- 
oped in which the parts that were most aggressively sought were 
precisely the motors and sensors that Maria's group did not 
value, while the parts that were least valued by the aggressive 
traders were the pretty pieces most suitable for building houses. 
Maria was enjoying herself in many ways. Exploiting the market 
to get the materials for a large and magnificent house gave her a 
certain entrepreneurial pleasure; solving geometric and technical 
problems of construction gave her a source of intellectual plea- 
sure, and the form being taken by the product of all the work, 
the house, gave her aesthetic pleasure. She had found a niche. 
Would she settle into it and stay there? 

No! By the second week there were signs of yearnings in other 
directions. A desire to enter the world of technology was showing 
itself in the way the girls looked at classmates' projects. By the 
third week observers saw the desire in a more concrete form when 
they noticed that a tiny light was blinking on and off in the deep 
recesses of the house. It was as if these girls wanted to take hold 
of the technology, but had to do so with great discretion to get 
past internal censors. The idea of doing anything technological 
went directly against the grain of their sense of identity as girls in 
very traditional families. They wanted to take hold of the technol- 
ogy, presumably they had always wanted to take hold of the 
technological side of the world, but had to do it, as it were, behind 
their own backs, almost invisible to themselves as well as to 

Although the boys with their noisy trucks might not have con- 
sidered a blinking light much of a project, the house builders were 
proud of their achievement, which was, in fact, less modest in its 
realization than in its appearance, since it brought them face to 
face with the computer. The story of the skirmishes they won in 
this encounter with the ways of computers is worth following in 
some detail. 

120 • The Children's Machine 

The story opens with an easy step. To begin with, they had to 
connect the light to the interface box, which was not really differ- 
ent from plugging a lamp at home into an electrical outlet. The 
next step brought immediate gratification: Making the light go on 
and off by typing the words ON and OFF at the computer felt very 
different from turning a switch! By now the excitement was great, 
and this was fortunate because it gave the group a taste of success 
that carried them through the difficulties they would meet. 

These began with the natural proposal to make the lights blink 
on and off automatically. The instrument available for this was the 
Logo language, the elements of which the girls barely knew from 
work with graphics that had started a few weeks before. One of 
them knew enough to type: 


The computer replied with an "error message," indicating that 
it was necessary to say how many times. They changed the in- 
struction to: 


This time the computer did not complain; the instruction was 
in grammatical Logo and the computer carried it out, but in a way 
that would be a lesson on how to interpret the adage that comput- 
ers do exactly what they are told to do, neither more nor less. This 
is true enough in one sense. Computers do indeed do what they 
are told to do. But what they are told to do is not always what one 
thinks one is telling them to do. Nor is what they do always what 
it seems to be. 

In this case, the computer did not seem to have done what it 
was told. The light came on and went off, leaving the eager 
observers waiting expectantly for the second blink, which never 
came. What was happening? The girls, surprised and frustrated, 
responded in a way analogous to a common habit of talking 

An Anthology of Learning Stories • 121 

louder to people in a foreign country who don't understand a 
request in English: They made the command more insistent by 
increasing the number of blinks they thought they were telling the 
computer to make: 


The change didn't solve the problem, but it had an effect that 
gave them something to think about. The light still came on only 
once but stayed on for a longer time before going off. "It doesn't 
know the difference between lots of times and a long time," said 
one of the girls. "Yeah!" "It's stupid." They all laughed, but plea- 
sure in their theory of the computer's behavior was soon replaced 
by frustration; it felt good to blame the machine and to have a 
sense of understanding its perverse behavior, but the lights were 
still not blinking. However, the theory did lead to constructive 
actions. The first action was to try to confirm the theory by trying 
REPEAT 10000. Yes, indeed, the light stayed on longer, as far as 
they could judge ten times as long, but still performed just one 
on-off cycle. Suggesting an experiment is a good quality for a 
theory; and on this occasion the experiment worked, seeming to 
confirm the theory. But the goal of making the lights blink had not 
been achieved. 

Interestingly, what brought the goal closer was another, even 
better, quality of a theory: giving rise to insight by suggesting 
fruitful questions. Someone believed the theory sufficiendy to ask, 
"But how can that happen? How can lots of times get confused 
with a long time?" The stupidity of machines amused the girls as 
a first answer, but its attractiveness as an explanatory principle 
soon wore thin. "I know," one of the girls said, "it goes so fast you 
can't see it. Computers go very fast. It really is doing it ten thou- 
sand times but they all run together." Aha! The insight proved its 
quality by leading to amusement and to action that would solve 
the problem. Maria said: "Yes, it's going too fast; tell it to slow 
down." After some chuckling at the idea that ten thousand blinks 

122 . The Children's Machine 

Z n T St " 10 * iBViSible ' —ne asked "How- 

andanothercam e inwith,"Waita S ec.. Hey that's i«Z V 
you can say WAIT in Logo." So they typed ^ 


girls had P S2tr T ? C C ° mpUter: JUSt as 
repeat, they nZ o^ ° * ^ ^ h ° W times to 

We about ™Z S ZTrU ^ r ,0ng t0 Wait So " kno ™"8 * 
out Logo s ways, they tned "giving WAIT a number": 


that day Y ^ bm Were to ° ela ^d to fiddle with it 


Making a single light blink indefinitely in the denrh t , 
house was a small sten into th ,L , pths of a ^8° 

broken the ice "I* ^IT™ ^ ° f techno, °gy. but it had 
lights in thehou^A ZkZT^ *** TO "»* b,inki <* 

pieces: They now wam*H 7 for P rettier ^8° 

-m. This l~ I" ^ ^ ^ ^ 

brought them into oil ^ £ ri * ht *>' 

of mechanical engine «n g ^ther f n ^ ^ " ^ ^ 
but before their ^7^0^ ^^ P"*™*^ 
technical barrier «^7«J? J? , ^ had crossed 

35 Wdl 3nd had bui]t themselves in addition to a 

An Anthology of Learning Stories • 123 

work of art and technology a first, albeit shaky, bridge across the 
cultural barrier. 

It is a useful metaphor to think of Maria as crossing a single 
barrier, one that separates her from all those activities that have 
been programmed into her sense of identity under the labels "I 
can't do that" and "that's not for me." Every time she crosses the 
line, she comes closer to understanding that these labels are not 
immutable. Knowing that one can exercise choice in shaping 
and reshaping one's intellectual identity may be the most em- 
powering idea one can ever achieve. For me the story of Maria 
has become emblematic of something more than this idea in its 
elemental form. It carries messages about how to exercise the 
choice. Maria might have decided at the outset to bite the bullet 
and build a truck like the boys. It is more than likely that doing 
so would have led to a distasteful experience and reinforced her 
deeper sense of what isn't for her. Instead she followed her 
good instincts, engaging in activities that felt right for her, while 
keeping herself open to an evolution in a new direction. The 
problem for educators is how to enhance and extend all aspects 
of what we see in the story. Designing Lego-Logo was a small 
but instructive step toward knowing how to provide material 
that will serve well as a technological infrastructure for suitable 
learning environments. But the more important side of the prob- 
lem is nurturing the right kind of culture of learning. 

Some educators might think that the process could have been 
made more efficient, and more comfortable, if a teacher had sug- 
gested the blinking light project at the outset. There are even 
researchers who dream of programming a computer to "diag- 
nose" individual difficulties in such situations and prescribe paths 
to learning. I fear that this line of thinking risks missing an essen- 
tial fact: What was empowering for Maria and her friends was not 
making the lights blink but finding their own way to get around 
their own internalized obstacles. Although a teacher might, of 
course, have given some guidance in this, it is hard to imagine a 

124 • The Children's Machine 

more delicate teaching task or one that I would be less inclined to 
entrust to any contemporary computer's power to make decisions 
As a teacher I would see my best contribution as reviewing the 
story afterward in a way that would consolidate the students- 
awareness of how well they had done. 

For example, I would want to be sure they recognized that 
building the house was an excellent strategy for mobilizing their 
own strengths and their own self-confidence in a difficult situa- 
tion. The topics under discussion would not be Lego and lights 
and motors but ways of dealing with intellectually difficult or 
uncomfortable situations. They might include talk about strategies 
or solving problems and managing projects. And if I felt emotion- 
ally safe enough with the students, I would talk about the gender 
and ethnic issues. The extent to which I would politicize the 
discussion would depend on the context, but if the students took 

whTthTh HT ld Cenainly ab ° Ut the P° litical of 
what they had done, not only because I think that the political 

dimension should not be hidden but also because without it the 
work^Th ^ appreciate the intellectual power of their own 

nm H l d ^ml virtue of the Lego-Logo workshop was 
providing elbow room for these students to take what they found 

Me"" r PCrSOnal W3y - ° ne faCt ° r th3t made this Possi- 

nel Trh«r 8 3ttitUde ° nC C ° Uld CaU demandin * P-^ve- 
ness_ Children were expected to work hard on a project related to 

the themes of the workshop but were given very wide latitude in 

choosing the project. If permissiveness were the only factor the 

same teaching attitude could solve all educational problems It 

Z2 d Tt e T do{ factor is inherent in the 

rial and m the learning culture that it supports. Many teachers 
stnve to bring into their traditional classes something very like the 
cent" 8 attUU f K° f thlS WOTkShOP - BW the P«ntaLL is de- 
children to fit into the straitjacket of the traditional curriculum, 
especially ,n subjects like math and science where the elbow room 
for personal appropriation is so narrow. 

An Anthology of learning Stories • 125 

Funny Learning 

Debbie connects with fractions and Maria with engineering. 
Each story has a main plot with a clearly stated happy ending. 
But a fine texture of smaller connections is just as important. 
Maria finds it funny that a thousand events can happen in a split 
second; one thousand may be a big number but it can be a tiny 
piece of time. The concept is important in itself. Much more 
important is the fact that she appropriated it through a joke con- 
necting mathematics with humor, something for which there is 
little scope in school math. 

A friend's conversation with his young daughter illustrates how 
a mix of the serious and the humorous happens spontaneously in 
certain family cultures. This favors mathematical development by 
slowly building a rich web of connections. 

Child: Daddy, do you know that two is half of four? 
Father: That's interesting. Yes, I do know. Do you know 

what is half of six? 
Child (thinks for a while): Three. 
Father: And what is half of three? 
Child (thinks for an even longer time): Which half? 
Father (who has to do the thinking this time to catch on): 

The big half. 
Child: Two. 

Father: And what about the other half? 
Child (with an air of who-do-you-take-me-for): One, of 

One would miss the point of the story without knowing the 
atmosphere of this family, where such things are both taken very 
seriously and treated with humor. "Which half?" could become a 
joke in the family culture, and through many such little incidents 
numbers would be woven into the family culture as something to 

126 • The Children's Machine 

play with, to joke about. What is inrerp«rin« ■ 
learned th* L , interesting here is not that a child 

learned the Important Concept that even numbers have exact 
halves and odd numlvrc H™> t wn, • • ct 
provides nnZ , , 15 lnterestin 8 * that a family 

TclTs 1 3™ ^ ^P 0 *^** *> appropriate mathemat 
ics as a warm and cozy dimension of life connected to other 
dimensions with which they fee, comfortable 

view q oft w f ^ inddent An 6Xam P le -^en the 

that IST* 1 ? T CMd ' ° aWn ' W3S Pla ^ with a Logo program 
mln rt ° b r S ° n ^ t0 be ^igned'and setl 

Z h ^ leaving paths made kinetic patterns like 

*nr£n°r°r' si 7i r tnan) those that had f ~ 

J* one finger hidden be^"^^^^ 
she was ty ping . Everyone lQoked said^W 

ESSiSSi Dawn said " Look - ,oold and * - k '^ 

had ^2 f ^ f 01 k N ° thin8 W3S happen ^ b — s ^ 
7 861 Speed °- SJow] y » became clear that zero was a soeed so 
that standing still is moving-coving at speed Zo ' 

cover, Was it Xth^d 

st^TundTt f r C ° U,d ^ aS 

STdSU " ^ ^ ° n,y Child to ^ ™^e 

mis discovery. Nor was a computer needed. Indeed a noil of 

Parents at a meeting of teachers showed that P e! ps aTly 

/)« Anthology of Learning Stories • 127 

as one in ten of those who had children of their own had noticed 
a moment of excited joking of the form, "Are there any snakes in 
this house? Yes there are, there are zero snakes, " 

The fact that many children make a similar discovery without 
the computer increases rather than diminishes my enthusiasm for 
the episode with Dawn, It shows that this is not a strange oddity 
about computers; it is part of the development of mathematical 
thinking. The computer probably contributes to making the 
discovery more likely and certainly to making it richer. Dawn 
could do more than laugh at the joke and tease the teacher and 
her friend: Accepting zero as a number and accepting standing still 
as moving with zero speed increased her scope for action. A little 
later she would be able to write programs in which a movement 
would be stopped by the command SETSPEED 0. Even more 
interesting, the joke can be extended. The turtle will obey the 
command FORWARD -50 by going backward fifty steps. Simi- 
larly, the command to go back a negative amount will make the 
turtle go forward. So, negative numbers are numbers too, and 
their reality grows in the course of playing with the turtle. 

Looking at the fine texture of Maria's experience shows other, 
different kinds of opportunity for incidental learning. One of these 
is handling experiments. The girls replay a situation that occurs 
sover and over again in science. First they are puzzled — and this 
in itself makes the situation far more real than the usual school lab 
science experiment, which typically studies a question that has 
bothered nobody for the past hundred years. They discuss hy- 
fpotheses and eventually decide on one that seems likely. They 
mount an experiment to test their hypothesis. The hypothesis is 
confirmed in essence but requires some modification. Sharpening 
;the hypothesis leads to new developments that the girls pursue. 
This is very much like "science." It is very much not like "School 

My stories about Debbie and Maria have a "remedial" aspect: 
P"heir protagonists are presented as improving an initially poor 
relationship with an area of knowledge. Being remedial is not 

128 * The Children's Mach,ne 
really of the essence in the «tnrf« r 

lowing how an initial h^T^T* - 
tess, they show early JZ, Z ?f Tu ? ^ Nev erthe- 
matics or technolo^ The nL ^7 ™* h 

ma the- 

more developed relationship *"* *" ^ ° f 3 mu <* 

Ricky's Invention 

Ricky was a fourth-grade student when he fW 

« MIT. I don't know what he dTd !n £ fi ^ Le *° 
aware of his work when he had SCSSi ° nS - 1 beca ™ 

that would move by Z^on ^ * ^ t0 make a ~bot 

A washing machine that has " tend to m — 

-8 a lot of noise and ° ™k- 

tends to move about u^Z rLT^ also 
sometimes called "traveiinT" 7? n ^ ThiS P he "™enon, 
be overcome either by ridudnt the I M 3 nUiSa " ce » 

-choring it more securely ^^2° ° f the de -e, or by 
at a vibrating Le go construction and7 h h ^ He Iooked 
» ^vel as a means of SS^T^W-T 
serendipity-turnmg the chance oh ^ 3 dear Case of 

often observed SpIZI^" t0 « - 

nations and are aiTd 2^?^ Cha - ob- 

saence and elsewhere is 90 percent luck r , * SUCCCSS in 

without some other mgredie^^t ^ *** " 0t W off 
« it, energy, per.iste^^^ UnderStand a ^ pur- 
the -nse of a supportive en^en ST*' ^ ^ 
stnking fashion. ™nment. R, c ky shows all of them in 

Having observed that a Leoo m > 
question was hot i teTlT * 
made ,o vibrate more effecII ^ V "" i " ,0a How «"> » be 

An Anthology of Learning Stories • 129 

in many other situations where I was able to observe him at work 
is to look for familiar situations where what you seek is well 
represented. Ricky found one by swinging his arm violently 
around. The movement of the arm caused his body to move in a 
seemingly random fashion. If this happened faster it would be 
"vibration." So he set out to provide the Lego motor with an arm. 

This obliged Ricky to consider the question: What is an arm? 
The human arm is a complex system. Ricky simplified it. For his 
purpose, what was relevant was that the upper arm could turn 
about a shoulder and swing the lower arm in an uncontrolled 
way. So he looked around for Lego pieces that would simulate 
these features of the arm. It worked. The Lego motor equipped 
with this arm vibrated more and moved more. 

The next step was to build a vehicle that would use this source 
of locomotion. Ricky's idea was to make a platform with legs, 
mount the motor on the platform, and let it vibrate. This construc- 
tion turned out to have a fatal bug. When the motor was turned 
on it vibrated so forcefully that the entire contraption flew apart — 
Lego pieces flew off in all directions. 

What could be done? Ricky considered two courses of action: 
Reduce the vibration or increase the resistance of the structure. 
Obviously, the second course seemed more attractive. But how 
Was it to be executed? 

f The first idea was to add many braces and generally strengthen 
ifhe whole thing, but it soon became apparent that this would 
make it so heavy that it was unlikely to move. Then came the next 
brilliant idea: Make it small and compact. 
& The motor still vibrated. The device did not fly apart. It even 
pnoved a little, but fell over as if it were tripping on its own feet. 
Stop the motor. Stand it up. Try again. Same result. Now what? 
jf The solution came from a classmate. Give it feet! Why? H ow? 
gPebate quickly gave way to action. It was given feet by using Lego 
jpheels as shoes, as shown in the sketch. There was a momentary 
jgdoubt about whether it was cheating to use wheels, since this -was 
po be a wheelless vehicle. But it was quickly resolved: These 

130 * THE Ch «"«n's Machine 

wheels were n nt k ■ 

we* , P™Pose ,ust as we „, bu[ ^ 

w accepted i, was e „j„ y ^ " were Once the idea 

■fcky s descn p don of nis wort wh 3 Promto ™ P*n 

anyone who asked ' he «" "elided ,o g iv " ,o 

— Aga.n d.e raomem Qf <fc ^^» P* CouJd , be 

^ as lost the excite- 

An Anthology of Learning Stories .131 

mem, but suddenly everyone standing around it knew that when 
it was started it changed direction slightly. Physicists have a name 
for the cause of the jump: They call it conservation of anguW 
momentum. In practice, what this means is that when the mot 

t oZ n ZZ- ^ C ° nneCted ^ * has to 

the other way. This may seem unbelievable-which I hope is the 

case (except for those who have studied physics or dar^e) Z 

cause the statement goes against so many common observations 

But Ricky and his friends did not stop to worry about what phy" 

steer the robot by turning the motor on and off . 

Doing so required some skill but was nonetheless a solution 
The machine could be steered! 

Next problem: Could it steer itself to go in a more or less straight 

techno. , d 3CCeSS thCn t0 the SOmewhat proved 

technology we have today, he would have carried out the self- 
Bering project. As it happened, doing so with the means at his 
disposal was too messy and needed too much help, so he pre- 
ferred to turn his interest in other directions. 

S h ba ; Cky — working at a more advanced level, his 
method had a great deal in common with what we saw in the 
other st ones. Like Debbie and Maria and like the practitioners of 
kitch th ^ worked by feeling his way. He did'not follow an 
rea^' H f * ^ W & a " d Was co «« to 
rTof buifd ' rTT T a,, ° Wed 10 eVOlVC 38 he WOrked ^ ^d 
that purpose; he used what he found at hand, even taking plea- 
mi? 18 S ° met f 8 f ° r 3n alt ° gether dfcnt P-Pose. 
Ricky s manner of working, with its elements of improvisation 

"th i T17 T *f : ork in progress ' is a prime exam p je 

or what Sherry Turkle and I have called bricolage adaotine from 
anthropologist Claude levi-Strauss the use of a tn^ word 
whose nearest (but inadequate) translation might be "tinkering." 

132 • The Children's Machine 

Dirty Dancing 

not, as far as I know *Z "Actional feature film that was 
Stufly academics XaTv profess '°'ra' on learning. 

°C raigh l!T" em T °* U "°*odox method 

-vie ne 8 a j££ "JSl "Z^ '°° * ~ » 
I wanr , aeas about Educauon? 

eral culture as a source oH^T^ T ? C ° ^ » the 8 en " 

ences. This recommendation flJTf , PerS ° nal ex P eri " 
dimension of life, Z °? * * as a 

bi«ty. in all such ^^Ze^ZTZ' °' ^ 
tivity from works of P so P hlstlc ation and sensi- 

won^Sh ' ; he .rc o r novels ' ,hea,er ' pawn8 

«*y convey trutL as deep ^ and I ^ an " hCT 
P«toa„ K conduce ^ZTl™* aCCUra ' e * an - 
beUeveweea„iea m aJ u ~ nB ° SUCh t0piC5 ' ' 

d° so to a nearer extent "■^^^h""* ^ TOuW 
aspeel of art. Practiced emical discussion of this 

loo?S:Lta.7e^reStr y r* BOnl ^^ s ^ 
if they choose B ST' """"S flcU ° n ' Fot <™> 
knowledge, they can t T ^ ""^ " as a *»«* of 

Wbe M ^tr^tr "* ^ unc °- 

Popular culture. And if tee o7 earn "' 8 PKVaknt l " «* 

as parent „ ho Mu^^fT r^*"*"* ° r ^ «* 
-rely aifec, how learSg " ^ 

love story, m lts opening scenes we see 

An Anthology of Learning Stories • 133 

Jennifer Grey in the role of Baby, an idealistic student whose 
ungainly walk and posture carry the message that she was occu- 
pied with cerebral concerns when her peers were developing their 
sense of body and movement in physical activities. Baby is no 
dancer, and knows so litde about dancing that she seems not to 
have any idea of the magnitude of the learning that will be re- 
quired when she volunteers to substitute for the female partner in 
a spectacular dance act less than a week away. In fact, a critical 
teacher might attribute the same ignorance to the author of a story 
that shows Baby performing the act competently after a week of 
intensive work with the male partner (played by Patrick Swayze). 
For my part, I don't know whether this timing is credible, but I do 
know that it is much more likely to be achieved through a learning 
process like the one shown in the movie than through the kind of 
process practiced in School. 

Be that as it may, the connoisseur of learning will find more of 
interest in the quality of Baby's experience than in speculation 
about the time required to achieve her goal: What made the movie 
compelling for me was the credibility of the features of good 
learning it brings into the spodight. The fact that some of these 
features (among them possibly the speed of learning) are pre- 
sented in a heightened, larger-than-life form appears to me as a 
benefit (certainly not a fault) from the use of the artistic medium, 
just as the high drama of the action in Romeo and Juliet makes it 
more, not less, relevant to the human issues we meet in the lower 
drama of our own lives. 

The movie's action takes place in a resort in the Catskill Moun- 
tains, where one sees two classes of people, two kinds of dancing, 
and two kinds of learning. The staid, well-heeled guests are pam- 
pered in the hope that they will come back next year. The resort 
workers are disciplined and bullied by the threat that they might 
not. Although the resort is structured to keep the two classes as far 
apart as possible, such lines of segregation are seldom absolute, 
and in this case the action of the movie is precipitated by two 
crossings. Baby, brought by her parents to this place that has no 
attraction for her, restlessly wanders through its grounds and 

134 • The Children's Machine 

ously shel^ exSeZta Lt enc °»*'ed in her pre*, 
and has been abandoned by £ tab^T" I™"™ 

formless,, ,„ S r^TST 5£?f ^ "»* 
quences of steps, "Forward TwaS^ i T'"" ~ 

•slow...sJow o„iei, ' ' ' ™ w " ni ■•• «■* ■•■ together" and 

People dance Twe,,^' They're ^ " Saff ^ 

me deeper sense of what is H^n u . . 

dearer if we shift the focus ran A ' 1S ^ beCOmes 

dance. When dancim iwS. Z u to ,earnin 8 h ™ to 

b^^J^f^f bY f ° rmula * lends *** to a 
I think that anyone who Z U t0 teachi <*" 


is cleanly defined The e or ^ fox ~ * * 
side together, back sfde co^^lS^^T! ^ 
we'll do the forward promenade wiT u * 3 httle then 

Practice putting them togeTh e r ^ ° f *« We ' U 

The relationship between learner and teacher k u 
« - confined, on pain of dismissal fortk^ " ! 

technical work on mastering , 11 teacJle r, to impersonal 

snb„ y , ,he reSr^ be^ ~ aT ^ ^ 
learned is like a clean 1 een the ,earner and what is 

w*h minima, Impac „„ te leaJi's^^^ 

An Anthology of Learning Stories • 135 

We see something very different when Baby begins to work 
with the dance instructor. Although the movie does not make this 
explicit, it is safe to assume that her previous experience of dance 
lessons, indeed of lessons in general, would lead her to expect 
that the work would follow the pattern of clean learning. In fact 
she gets something very different. Learning "steps" is the least pan 
of it, though there is some of that as well. Her tutor tells her to 
"listen to the music like a heart," and uses their slowly developing 
erotic relationship to draw her into a different sense of space and 
of her body. He has her walk dangerously across a high and 
narrow log bridge to develop a sense of equilibrium, posture, 
and confidence. What is happening to her as she learns to dance 
is not confined to a cleanly delimited set of emotionally neutral 
skills. It certainly could not be described as a "program" in any 
ordinary sense of that word. It includes entering a new relation- 
ship with herself It includes changing her relationship with au- 
sthority, with her father, and with the upper-crust world in which 
her family lives. 

p is reasonable to ask whether the contrasting models of learning 
|hat I have called "clean" and "dirty" in the domain of learning to 
dance apply to other domains that are considered more abstract 
and intellectual. To feel out a response I shall probe the extent to 
pVhich a parallel can be made with other more Schoolish areas, 
|tarting with the most abstract, namely, mathematics. 

In some respects, on the clean side, the parallel works easily. 
Clean learning reduces dance to formulas describing steps, and 
pan learning reduces math to formulas describing procedures to 
populate symbols. The formula for a fox-trot box step is strictly 
analogous to the formula for adding fractions or solving equa- 
tions. The other components of cleanness in dance lessons also 
apply directly to school math. Emotions are kept out. The relation- 
ship between teacher and student is confined to the exchange of 
formation about the topic being studied. Certainly nothing verg- 
jjftg on the erotic is considered to have any role. 

136 • The Children's Machine 

On the side of dirty learning, the parallel might seem less clear. 
In representing Baby's learning as "dirty," I referred to bodily 
involvement, to overcoming fear, and to issues of social class. It 
might seem that these issues are intrinsically associated with dance 
but are not really part of what mathematics is about. I do agree 
that it seems so if one accepts the prevailing models of school 
math. But then it would also seem that dance is not related to such 
matters if one stays with the models of dance and dance learning 
that prevail in the guest's ballroom or in Arthur Murray's presenta- 
tion of education in ballroom dancing. It is necessary to do a little 
deconstruction to distinguish between aspects of mathematics 
that have been built into the School construction of what the 
subject is about and those that have a stronger claim. 

If one accepts what Brian and Henry were doing as math, the 
distance between math and dance is at least a little reduced, for 
they were doing something of both at the same time. They cer- 
tainly were bringing more of themselves into the picture than is 
envisaged in the clean math class. Maria was challenging a social 
affiliation. Debbie was changing her sense of herself, as indeed 
Brian and Henry were. What I think is quite clear is that in these 
situations we see children moving toward the position marked out 
by Baby's learning. If they don't go as far, it is not because school 
subjects are intrinsically different from dance but because Baby 
was in a situation to live her relationship with dance more fully 
than one could hope to see in today's schools. 

Instructionism versus 

I have tried to stay for as long as I could with a style one could 
loosely describe as concrete. The time has come to switch, 
although only for the space of one chapter, to a slightly more 
academic and abstract style so as to allow comparisons and inter- 
change with other points of view. In doing so I shall also work at 
I sharpening and formalizing (which does not necessarily mean 
| improving) mathetic ideas that I have introduced up to now 
1 mainly by way of stories. 

||; My preference for a concrete way of writing is not simply a 
literary tactic for saying what I could have expressed in more 
I abstract language. Rather, it is a case of making the medium the 
message. A central theme of my message is that a prevailing ten- 
dency to overvalue abstract reasoning is a major obstacle to prog- 
| ress in education. One of several possible formulations of my view 
I of how learning might become very different is that this will co»me 
fpbout through an epistemological reversion to more concrete 
I Ways of knowing — a reversal of the traditional idea that intellec- 
tual progress consists of moving from the concrete to the abstract. 

Moreover, I see the need for the reversal not only in the content 
|W what is learned but also in the discourse of the educators. Using 

134 • The Children's Machine 

-d 1-. been abandon*" ttby75£ '"the ^ 
nephe„ ; Baby's offer will altow her to faJe he!es^ T 
an abortion. esort and hay e 

quences of steps: "Forward WaS sid "'^ 
^edar w ^ ra £r d ™~ 

engagement of body, of energy, of passion ^ "* fU " 

deader JTsS 5 S ! C ' ea H ^ * 
dance. When ^^deflnX f "Z " TT* » 

dancing knows wLT*i,t,,te X IT" Ch °°' ° f ba " r00m 
* cleanly defined Th s« P 0^ ox ~ *. ^ 
-de togedter, bach brush sfde 

we'll do the forward promenade Wh™ c " Ihe " 

practice purring .hem t^Xr ^ b °* ^ «* 

The relationship between learner and teacher kv, ., ■ t 
« - confined, on pain of dismissal for th^achj '" ,' 

technical work on mastering , 11 ' to lm Peraonal 

most subtly the ITunn h * I ^ °' SKps ' ^ 
learned is fik'e a ? k™*" *» ' eamCT ™d what is 

with minima, hnpac, on the JZ^%£%£. 

An Anthology of Learning Stories • 135 

We see something very different when Baby begins to work 
with the dance instructor. Although the movie does not make this 
explicit, it is safe to assume that her previous experience of dance 
lessons, indeed of lessons in general, would lead her to expect 
that the work would follow the pattern of clean learning. In fact 
she gets something very different. Learning "steps" is the least part 
of it, though there is some of that as well. Her tutor tells her to 
"listen to the music like a heart," and uses their slowly developing 
erotic relationship to draw her into a different sense of space and 
of her body. He has her walk dangerously across a high and 
narrow log bridge to develop a sense of equilibrium, posture, 
and confidence. What is happening to her as she learns to dance 
is not confined to a cleanly delimited set of emotionally neutral 
j skills. It certainly could not be described as a "program" in any 
j ordinary sense of that word. It includes entering a new relation- 
ship with herself It includes changing her relationship with au- 
|thority, with her father, and with the upper-crust world in which 
fher family lives. 

fit is reasonable to ask whether the contrasting models of learning 
pat I have called "clean" and "dirty" in the domain of learning to 
pbnce apply to other domains that are considered more abstract 
|nd intellectual. To feel out a response I shall probe the extent to 
which a parallel can be made with other more Schoolish areas, 
parting with the most abstract, namely, mathematics, 
jlpn some respects, on the clean side, the parallel works easily. 
Clean learning reduces dance to formulas describing steps, and 
clean learning reduces math to formulas describing procedures to 
% manipulate symbols. The formula for a fox-trot box step is strictly 
analogous to the formula for adding fractions or solving equa- 
|tions. The other components of cleanness in dance lessons also 
apply directly to school math. Emotions are kept out. The relation- 
ship between teacher and student is confined to the exchange of 
formation about the topic being studied. Certainly nothing verg- 
|p8 on the erotic is considered to have any role. 

136 • The Children's Machine 

On the side of dirty learning, the parallel might seem less clear. 
In representing Baby's learning as "dirty," I referred to bodily 
involvement, to overcoming fear, and to issues of social class. It 
might seem that these issues are intrinsically associated with dance 
but are not really part of what mathematics is about. I do agree 
that it seems so if one accepts the prevailing models of school 
math. But then it would also seem that dance is not related to such 
matters if one stays with the models of dance and dance learning 
that prevail in the guest's ballroom or in Arthur Murray's presenta- 
tion of education in ballroom dancing. It is necessary to do a little 
deconstruction to distinguish between aspects of mathematics 
that have been built into the School construction of what the 
subject is about and those that have a stronger claim. 

If one accepts what Brian and Henry were doing as math, the 
distance between math and dance is at least a little reduced, for 
they were doing something of both at the same time. They cer- 
tainly were bringing more of themselves into the picture than is 
envisaged in the clean math class. Maria was challenging a social 
affiliation. Debbie was changing her sense of herself, as indeed 
Brian and Henry were. What I think is quite clear is that in these 
situations we see children moving toward the position marked out 
by Baby's learning. If they don't go as far, it is not because school 
subjects are intrinsically different from dance but because Baby 
was in a situation to live her relationship with dance more fully 
than one could hope to see in today's schools. 

Instructionism versus 

I have tried to stay for as long as I could with a style one could 
loosely describe as concrete. The time has come to switch, 
although only for the space of one chapter, to a slightly more 
academic and abstract style so as to allow comparisons and inter- 
change with other points of view. In doing so I shall also work at 
sharpening and formalizing (which does not necessarily mean 
improving) mathetic ideas that I have introduced up to now 
mainly by way of stories. 

I My preference for a concrete way of writing is not simply a 
literary tactic for saying what I could have expressed in more 
abstract language. Rather, it is a case of making the medium the 
•.message. A central theme of my message is that a prevailing ten- 
dency to overvalue abstract reasoning is a major obstacle to prog- 
ress in education. One of several possible formulations of my view 
of how learning might become very different is that this will come 
about through an epistemological reversion to more concrete 
w »ys of knowing — a reversal of the traditional idea that intellec- 
tual progress consists of moving from the concrete to the abstract. 
[Moreover, I see the need for the reversal not only in the content 
*f what is learned but also in the discourse of the educators. Using 

138 • The Children's Machine 

a concrete mode of expression myself allows me to show as well 
as say what I mean by this, and contributes to a richer sense of 
what makes concrete thinking powerful. However, it is not sur- 
pnsing that the concept most in need of a more abstract formula- 
tion is concreteness" itself. 

In the discourse of education, the word concrete is often used 
»n its everyday sense. When teachers talk about using concrete 
materials to support learning the idea of numbers, one easily 
understands that this embraces such methods as using wooden 
Clocks to form number patterns. But the word has also acquired 
more specialized meanings, of which the most prominent is 
closely assoaated with Jean Piaget's famous (or, in some circles 
famous) theory of stages. Unfortunately the two kinds of use are 
often confounded: It is easy to fall into the trap of reading Piaget 

nJ, IT d ° rdina,y mCanin S' and the f ^V h sup- 
ported by the many books written in a patronizing tone on the 

ines of "Piaget made easy" for teachers. In fact, P* get is doing 
somethmg more complex and much more interesting when he 
describes the thinking of children of elementary school age as 

concrete." This is as much a technical term as the physicists use 
o the word force or psychiatrists' use of the word depression-in 

t^ZT S b£ ^"^tood unless one real- 

izes that the words get a special twist from theories that often go 
against the grain of common sense. Piagefs concept of "concrete 

emerfdT T ^ * the ° re * al P™P«live that 

emerged slowly, and not always consistently, in the course of an 
enormously productive lifelong enterprise of research. We shall 
have to d 1S entangle this very insightful concept from certain more 
problematic aspects of Piagefs theoretical constructions, in partic- 
ular his nouon of "stage." The opposition of educational philoso- 

for 1 !T ° f Chapter P f ° vides a ^od context 

for pinning down what "concrete intelligence" means in Piagefs 
theoretical framework. 

The suffix -ism is a marker of the abstract and its presence in the 
title reflects my shift in intellectual style. The word instructions 

htstructionism versus Constructionism • 139 

is intended to mean something rather different from pedagogy, or 
the art of teaching. It is to be read on a more ideological or 
programmatic level as expressing the belief that the route to better 
learning must be the improvement of instruction — if School is less 
than perfect, why then, you know what to do: Teach better. 
Constructionism is one of a family of educational philosophies 
that denies this "obvious truth." It does not call in question the 
value of instruction as such. That would be silly: Even the state- 
ment (endorsed if not originated by Piaget) that every act of 
teaching deprives the child of an opportunity for discovery is not 
a categorical imperative against teaching, but a paradoxically ex- 
pressed reminder to keep it in check. The constructionist attitude 
to teaching is not at all dismissive because it is minimalist — the 
goal is to teach in such a way as to produce the most learning for 
the least teaching. Of course, this cannot be achieved simply by 
reducing the quantity of teaching while leaving everything else 
unchanged. The principal other necessary change parallels an 
African proverb: If a man is hungry you can give him a fish, but 
it is better to give him a line and teach him to catch fish himself. 

Traditional education codifies what it thinks citizens need to 
know and sets out to feed children this "fish." Constructionism is 
built on the assumption that children will do best by finding 
("fishing") for themselves the specific knowledge they need; orga- 
nized or informal education can help most by making sure they 
are supported morally, psychologically, materially, and intellectu- 
ally in their efforts. The kind of knowledge children most need is 
the knowledge that will help them get more knowledge. This is 
why we need to develop mathetics. Of course, in addition to 
knowledge about fishing, it is as well to have good fishing lines, 
which is why we need computers, and to know the location of 
rich waters, which is why we need to develop a large range of 
mathetically rich activities or "microworlds." 

Take mathematics once more, to see the general issue in its 
most extreme form. It is obvious that as a society we in the United 
States (and most places in the world) are mathematical under- 

140 * The Children's Machine 

*a l™ S ^ V 'r *!■ <" -nathetnatics „ „„ 

■° teSSS^ " d ° ra n °' **» to « *= only route 
-oute goTwTZ" *e unpmvemen, of inaction. Anoeher 

which teyZfr h m>y iMerc5,in 8 "licroworlds to 

Debbie S orZ Xr"n " "* " *** — » - 
team sonXT^XZ 2 ' fchikta T «" «> 

do so e^f^T^T ° PP0nunl '>' '° 1«» " in use, they 

difflcuhreo *^ ^!' 5 T f . H,ample ' -» '«™ 

use "~~^xtrr s ote 

likes ,o .eaTjueircKnl" T ' nSm,a " >n is ta "obody 

-keteaehtogbte?^'^;^— °"' S ' — 
best of both worlds necessary, thus achieving the 

and L^izzgzzs rr r ng ,he compuK ' 

different from something that used mt , g " Veiy 

I" the 1960s, at the same timTas * e N^w Mat"^ 
its ^ ^ was fashionable to sly t^aUt ^ T™**' 
teach "the process of scientific thmW" IZ f ° 
tific content. The smnihcZ Z 8 than ^ Particular scien- 
divorced from «J5t^*S? t ^ ^ 
Debbie learned were even Z^ZZ^TZT" 8 ** 
every possible sense than th i . . and con crete in 

quired^y usmgTem kn ° W,edge abOUt fraCtio " s ** ~ 

Debbie's success in thp t^t ™ i 


/nstructionism versus Constructionism • 141 

to read Ivan Illich's Deschooling Society, again in the spirit of 
seeing an idea starkly through its extreme form. Illich eloquently 
states his case that the principal lesson School teaches is the need 
to be taught. School's teaching creates a dependence on School 
and a superstitious addiction to belief in its methods. But while 
School's self-serving lesson has pervaded world culture, what is 
most remarkable is that we all have personal experience and 
persona] knowledge that go against it. On some level we know 
that if we become really involved with an area of knowledge, we 
learn it— with or without School, and in any case without the 
paraphernalia of curriculum and tests and segregation by age 
groups that School takes as axiomatic. We also know that if we do 
not become involved with the area of knowledge, we'll have 
trouble learning it with or without School's methods. In the con- 
text of a School-dominated society, the most important principle 
of mathetics may be the incitement to revolt against accepted 
wisdom that comes from knowing you can learn without being 
taught and often learn best when taught least. 

Kitchen math points up the same moral; it shows that a large 
number of people have learned to do something mathematical 
without instruction — and even despite having been taught to do 
something else. Indeed, it may even suggest that there is no real 
crisis in education after all, since people with a will do find a way 
to learn what they need! 

Of course, this complacent suggestion is not serious. Pointing 
to the use of mathematical methods that were somehow devel- 
oped without being taught cannot justify educational compla- 
cency: Kitchen math and the like are wonderful demonstrations of 
people's mathetic capacity, but they are extremely limited. The 
conclusion to be drawn is not that people manage anyway and so 
do not need help, but rather that this informal learning points to 
a rich form of natural learning that goes against the grain of 
School's methods and needs a different kind of support. The 
question for educators is whether we can work with this natural 
learning process rather than against it— and to do this we need to 

142 • The Children's Machine 

-pec, c r r„ °;r h ° o1 is a 

no. the failure of School but .he succ"^ ,h f T" " 
devdoped own metho * , J * * ° «■» »ad 

chologlsB, my word wU| J edU ^'° re <"> d cogn,hve psy- 
contemporaryeduca.ion a l!Z "hose 

youcol^rS'"^ 8 t rmation by ,d "° 8 * * 

your imerlocutor ™ " ^ K ' >" OU WOUld obsen '« 
has the connote™ „ f « conve y»ng. Constructionism also 

literal sen": ^"^2^" ^ ^ ~ ta the 
languages considers' I t 8 ? ^ pro »-8 
-de, and kitchen" as W ^ Pr ° grams ca « * 

my central mathetic te^T 1 COnstructed - One of 

"in the head" often ZnZ ^ * e construc *>n that takes place 

— d h y when k is 

what I P mean ~ S °I f^T ° f the U «-- Part of 

discussed, examined loh H , Pr ° dUCt Can be sh °™, 

u, examined, probed, and admired. It is out th™ 
co„ st ru caonlsm , mypereoMl ^ ^ 

Instructionism versus Constructionism • 143 

tivism, has as its main feature the fact that it looks more closely 
than other educational -isms at the idea of mental construction. It 
attaches special importance to the role of constructions in the 
world as a support for those in the head, thereby becoming less 
of a purely mentalist doctrine. It also takes the idea of constructing 
in the head more seriously by recognizing more than one kind of 
construction (some of them as far removed from simple building 
as cultivating a garden), and by asking questions about the meth- 
ods and the materials used. How can one become an expert at 
constructing knowledge? What skills are required? And are these 
skills the same for different kinds of knowledge? 

The name mathetics gives such questions the recognition 
needed to be taken seriously. To begin answering them I shall 
discuss and adapt somewhat to present purposes the ideas of two 
thinkers, Jean Piaget and Claude Levi-Strauss, who went as far as 
anyone in identifying large pockets of knowledge that are not 
learned in School's way and do not conform to School's idea of 
what proper knowing is. My purpose in discussing both of these 
authors here is to derive from them a technical sense of the notion 
of concreteness that will allow me to say that the important 
mathetic skill is that of constructing concrete knowledge. Later on 
I use this insight for another formulation of what is wrong with 
School — that its perverse commitment to moving as quickly as 
possible from the concrete to the abstract results in spending 
minimal time where the most important work is to be done. 

In his 1966 book The Savage Mind (whose French title, La 
pensee sauvage, should be read with an awareness that in French 
wildflowers are called fleurs sauvages), Levi-Strauss adopts the 
untranslatable French word bricolage to refer to how "primitive" 
societies conduct "a science of the concrete." He sees this as 
different from the "analytic science" of his own colleagues in a 
way that parallels the difference between kitchen math and school 
math. School math, like the ideology, though not necessarily the 
practice, of modern science, is based on the ideal of generality — 
the single, universally correct method that will work for all 

144 • The Children's Machine 

problems and for all people. Bricolage is a metaphor for the ways 
of the old-fashioned traveling tinker, the jack-of-all-trades who 
knocks on the door offering to fix whatever is broken. Faced with 
a job, the tinker rummages in his bag of assorted tools to find one 
that will fit the problem at hand and, if one tool does not work for 
the job, simply tries another without ever being upset in the 
slightest by the lack of generality. 

The basic tenets of bricolage as a methodology for intellectual 
activity are: Use what you've got, improvise, make do. And for the 
true bricoleur the tools in the bag will have been selected over a 
tong time by a process determined by more than pragmatic utility 
These mental tools will be as well worn and comfortable as the 
physical tools of the traveling tinker; they will give a sense of the 
familiar, of being at ease with oneself; they will be what Illich calls 
"convivial" and I called "syntonic" in Mindstorms. Here I use the 
concept of bricolage to serve as a source of ideas and models for 
improving the skill of making-and fixing and improving-men- 
ta constructions. I maintain that it is possible to work systemati- 
cally toward becoming a better bricoleur, and offer this as an 
example of developing mathetic skill. One sees the spirit of the 
true bricoleur most directly in the story of Ricky's ingenuity (and 
delight) in using I*go parts for purposes that were never imagined 
by their makers: a wheel as a shoe, a motor as a vibrator. One also 
sees Jn this use of u^j^ a microworld strongJy condudve tQ 

the skds of bricolage. And I see it in my experience with plants. 

Kitchen math provides a clear demonstration of bricolage in 
its seamle** connection with a surrounding ongoing activity that 
provides the tinker's bag of tricks and tools. The opposite of 
bricolage would be to leave the "cooking microworld" for a 

math world," to work the fractions problem using a calculator 
or, more likely in this case, mental arithmetic. But the practi- 
tioner of kitchen math, as a good bricoleur, does not stop cook- 
mg and turn to math; on the contrary, the mathematical manipu- 
lations of ingredients would be indistinguishable to an outside 
observer from the culinary manipulations. Thus kitchen math ex- 

Instructionism versus Constructionism • 145 

hibits the quality of connectedness, of continuity, that I have 
presented several times as so powerfully conducive to learning. 
This embeddedness sharply illuminates the relationship between 
the mathetic question of instructionism versus constructionism 
and the epistemological question of analytic science versus bri- 
colage. Analytic principles such as multiplying IV2 by 2 A are 
routinely taught through direct instruction in math. But the close 
association of kitchen math with the kitchen suggests that it is not 
natural, even if it is possible, to "teach" mathematical (or any other 
kind of) bricolage as a separate subject. The natural context for 
learning would be through participation in other activities than 
the math itself. 

A comparison between Debbie and kitchen math brings out the 
special role of the computer in doing this. I have no doubt at all 
that increased skill and confidence would come to many people 
if they engaged in more respectful and thoughtful talk about their 
learning processes in cooking, gardening, home maintenance, 
games, and participation in sports whether as player or spectator. 
None of this absolutely requires computers. What we see in expe- 
riences like those of Debbie or Maria or Brian is how the computer 
simply, but very significantly, enlarges the range of opportunities 
to engage as a bricoleur or bricoleuse in activities with scientific 
and mathematical content. 

The phases of Debbie's experience show an expanding exten- 
sion of engagement and competence through a bricoleurish type 
of appropriation. In the first phase we see her engaged in a 
familiar activity minimally transformed by being done on the com- 
puter. She writes poems using the computer as little more than a 
word processor. Then she decorates her poems much as she 
might decorate a paper page. It is only when she is thoroughly 
comfortable with doing this that she begins to do anything inter- 
esting with fractions. Then we see her engaged in activities that are 
concerned with fractions; but in the same way as kitchen math is 
not separate from cooking, these activities are not distinguishable 
in form from the poetry work. And it is precisely this continuation 

146 • The Children's Machine 

of the familiar into the new that brings her breakthrough to con- 
necting fractions with "everything." 

This praise for the concrete is not to be confused with a strategy 
of using it as a stepping-stone to the abstract. That would leave the 
abstract ensconced as the ultimate form of knowing. I want to 1 
something more controversial and more subtle in helping to de- 
mote abstract thinking from being seen as "the real stuff" of the 
working of the mind. More often, if not always in the last analysis 
concrete thinking is more deserving of this description and^ 

XsTZ serve in the role of too,s *" se -' lie <4 

fo^ll r C ° nCrete thinkin& For the confi ™ed bricoleur, 

formal methods are on tap, not on top. In the kitchen forma 

wolt buto * " 3 « "~ 

suring cups improvisations with spatulas and mea- 

Statements like this have brought down on my head accusa 

T* baShin8 -; ^ iSSUC iS « ^ I 

T^ZTTt and , know firethand ** ma - els of ab ^ t 

reasoning. I know its pleasures as well as its power. I also 
know a ltifying , can be tf k . s ^ I 

intellectual culture has traditionally been so dominated by the 
identifier, of good thinking with abstract thinking that Z 
achievement of balance requires constantly being on the look 
out for ways to reevaluate the concrete, one milht say ° t 
epistemological analog of affirmative action. 

nTnoTnl ,0 ° k0Ut imidiOUS *™ ° f ^tractness ^ 
may not be recognized as such by those who use them For 
example, styles of programming that are often imposed as ff 
they were simply "the right way" express a strong value judg- 
ment between the abstrarr an H t u ' 8 
things. concrete ways of doing 

In her book The Second Self, Sherry Turkle describes styles of 

to c~ 8 Us f by chi,dren who were *™ sumaJaTc^ 

to computers and a sufficient sense of freedom in developing a 
personal style: H « * 

Instructionism versus Constructionism • 147 

Jeff is the author of one of the first space-shuttle programs. He 
does it, as he does most other things, by making a plan. There 
will be a rocket, boosters, a trip through the stars, a landing. 
He conceives the program globally; then he breaks it up into 
manageable pieces. "I wrote out the parts on a big piece of 
cardboard. I saw the whole thing in my mind just in one night, 
and I couldn't wait to come to school to make it work." Com- 
puter scientists will recognize this global "top-down," "divide- 
and-conquer" strategy as "good programming style." And we all 
recognize in Jeff someone who conforms to our stereotype of a 
"computer person" or an engineer — someone who would be 
good with machines, good at science, someone organized, who 
approaches the world of things with confidence and sure intent, 
with the determination to make it work. 

Kevin is a very different sort of child. Where Jeff is precise in 
all of his actions, Kevin is dreamy and impressionistic. Where Jeff 
tends to try to impose his ideas on other children, Kevin's 
warmth, easygoing nature, and interest in others make him pop- 
ular. Meetings with Kevin were often interrupted by his being 
called out to rehearse for a school play. The play was Cinderella, 
and he had been given the role of Prince Charming. . . . 

Kevin too is making a space scene. But the way he goes about 
it is not at all like Jeffs approach. Jeff doesn't care too much 
about the detail of the form of his rocket ship; what is important 
is getting a complex system to work together as a whole. But 
Kevin cares more about the aesthetics of the graphics. He 
spends a lot of time on the shape of his rocket. He abandons his 
original idea but continues to "doodle" with the scratchpad 
shape-maker. He works without plan, experimenting, throwing 
different shapes onto the screen. He frequently stands back to 
inspect his work, looking at it from different angles, finally set- 
tling on a red shape against a black night — a streamlined, futur- 
istic design. He is excited and calls over two friends. One ad- 
mires the red on the black. The other says that the red shape 
"looks like fire." Jeff happens to pass Kevin's machine on the 
way to lunch and automatically checks out its screen, since he 
is always looking for new tricks to add to his tool kit for building 

148 • The Children's Machine 

programs. He shrugs, "That's been done." Nothing new there, 
nothing technically different, just a red blob. 

By the next day Kevin has a rocket with red fire at the bottom. 
"Now I guess I should make it move . . . moving and wings 
... it should have moving and wings." The wings turn out to be 
easy, just some more experimenting with the scratchpad. But he 
is less certain about how to get the moving right. Kevin knows 
how to write programs, but his programs emerge, he is not 
concerned with imposing his will on the machine. He is con- 
cerned primarily with creating exciting visual effects and allows 
himself to be led by the effects he produces. 

The supervaluation of the abstract blocks progress in educa- 
tion in mutually reinforcing ways in practice and in theory. In 
the practice of education the emphasis on abstract-formal 
knowledge is a direct impediment to learning— and since some 
children, for reasons related to personality, culture, gender, and 
politics, are harmed more than others, it is also a source of seri- 
ous discrimination if not downright oppression. Kevin is lucky 
to be in an environment where he is allowed to work in his own 
style. In many schools he would be under pressure to do things 
"properly," and even if his way of working were tolerated, there 
might be a snide sense that this is because he is "artistic," said 
with a tone that implies he is not a serious academic student. For 
example, in interviews reported in a paper written jointly with 
me, Turkle was told by a female student that the pressure to 
follow Jeffs kind of "hard" style was so great and so contrary to 
her sense of herself that she "decided to become someone else" 
in order to survive a compulsory course. Others in a similar situ- 
ation simply dropped out. 

Furthermore, the supervaluation of abstract thinking vitiates 
discussion of educational issues. The reason is that educators who 
advocate imposing abstract ways of thinking on students almost 
always practice what they preach— as I tried to do in adopting a 
concrete style of writing— but with very different effects. 

Instructionism versus Constructionism • 149 

A simple example is seen in the formulation of research ques- 
tions. In front of me is a stack of learned papers, filled with 
numbers, tables, and statistical formulas, with titles such as "An 
Assessment of the Effect of the Computer on Learning." Their 
authors would be indignant at the suggestion that their work is 
"abstract." They would surely say that the shoe is on the other 
foot: They have produced "concrete numerical data," in marked 
contrast with my "abstract anecdotal philosophizing." But how- 
ever concrete their data, any statistical question about "the effect" 
of "the computer" is irretrievably abstract. This is because all such 
questions depend on the use of what is often called "scientific 
method," in the form of experiments designed to study the effect 
of one factor which is varied while taking great pains to keep 
everything else the same. The method may be perfectly appropri- 
ate for determining the effect of a drug on a disease: When re- 
searchers try to compare patients who have had the drug with 
those who have not, they go to great pains to be sure that nothing 
else is different. But nothing could be more absurd than an experi- 
ment in which computers are placed in a classroom where noth- 
ing else is changed. The entire point of all the examples I have 
given is that the computers serve best when they allow everything 
to change. 

The point of abstract thinking is to isolate — to abstract— a 
pure essential factor from the details of a concrete reality. In some 
sciences this has been done with marvelous results. For example, 
Sir Isaac Newton was able to understand the motions of the earth 
and the moon around the sun by representing each of these 
complex bodies by a concretely absurd "abstraction"— by treat- 
ing each body as a particle with its entire mass concentrated at one 
point he could apply his equations of motion. Although it has 
been the dream of many psychologists to possess a similar science 
of learning, so far nothing of the sort has been produced. I believe 
that this is because the idea of a "science" in this sense simply 
does not apply here, but even if I am wrong, while we are waiting 
for the Newton of education to be born, different modes of under- 

150 . The Children's Machine 
standing are needed. Specifically, in my view we need a method 

Ztl all r us to stay c,ose to concrete s^oZ 

Not long ago this suggestion would have been seen as incon 
-tent with the very idea of the scientific method. Howler TZ 
Pas few decades anthropologists have been more S£t d£ 
Lev.-Strauss was in examining the actual behavior of scfent L^n 

Ws In li Bnm ° LatOUr " °" e ° f the ^4 

the Z lZe lfT ement ' findS ^ ^ thCOretiCal Hne b — 
he science of the concrete and analytic science is blurry and 

frequently transgressed by ways of thinking and actingZ are 

closer to what I^vi-Strauss describes as pLee sauval than to 

scTentTfic meTd" ^ ° f ** « 

eX a^ *" 7 St ° f US have been taught in school is 

r^d L nh° 87 r° Cl r ed ^ ^ taUght in scho ^ »d 

ofslnce For Z / ^ " ^ ^ pfaCtice 

self riSr,!' ' ^"S^ 55 ' 8 " *8*nd dichotomy' with its 

self-righteous certainty should be replaced by many uncertain and 
unexpected divides." uncertain and 

Such observations have come from many other sources-in 

ceTfsLTnT S H h0larS ' ^ ^ that * 
ence ,s strongly androcentric, and Sherry Turkle and myself who 

have observed that some of the best professional programmers 

s " Kevin than ,ike jeff - ^seirr; 

sss&sr and they have muitipie 

The simplest and most immediate observation, from an instruc 

r: p 0 f r f t is ; he need to * chiid ™ * ~z 

image of the nature of science Th*» u 

5>ooi and" T C f aCt T' 3 g ° al tha ' dMS *<* «' «»° 

to bnng about these changes in science education both for the 
handed re aso„ of respect for ,™h ,„ educatL and ^ 

Instructionism versus Constructionism » 151 

dally, for the mundane reason that the image traditionally pre- 
sented repels students who would be attracted to the life of sci- 
ence if they only knew what it was really like, and to scientific 
thinking if they only knew how much it was like their own. 

From a constructionist point of view there is a deeper implica- 
tion, which I introduce by reopening the discussion of some 
important observations of children by Jean Piaget and his col- 
leagues. Essentially, Piaget had made the same observation as 
Levi-Strauss, except that where the anthropologist had looked at 
la pensee sauvage in distant societies, Piaget looked at la pensee 
sauvage close to home, in children. What they both saw was 
thinking that differed from "our" norms and yet had a degree of 
inner coherence that forbade dismissing it as simply erroneous. 
Both saw their findings as an important discovery of an unsus- 
pected way of thinking; both gave what they saw a name, each 
using the word concrete — in one case as "the science of the 
concrete" and in the other as "the stage of concrete operations." 
Both set out to investigate the workings of concrete thinking 
paralleling the investigation of laws of abstract thought that had 
been studied since ancient Greek times. Both gave us valuable 
insights into the workings of a nonabstract way of thinking. And 
both had the same blind spot. They failed to recognize that the 
concrete thinking they had discovered was not confined to the 
underdeveloped — neither to Levi-Strauss's "undeveloped" socie- 
ties nor to Piaget's not yet "developed" children. Children do it, 
people in Pacific and African villages do it, and so do the most 
sophisticated people in Paris or Geneva. 

Moreover, and this is what is of the most central importance, 
the sophisticates do not resort to "concrete thinking" only in their 
preliminary gropings toward solving a problem or when they are 
operating as novices outside their areas of expertise. As I noted in 
citing Latour, features of what Levi-Strauss and Piaget identify as 
"concrete" are present at the core of important and sophisticated 
intellectual enterprises. It is hard to give examples without too 
wide a digression into a technical discussion of a particular 

152 • The Children's Machine 

science. Feminist scholars who want to make a similar point in 
arguing that the supervaluation of the abstract is androcentric are 
fond of citing Evelyn Fox Keller's biography of the Nobel Prize- 
winning biologist Barbara McClintock. Keller's account gives an 
important role to an incident that is easily citable in nontechnical 
language: McClintock has become as well known for saying that 
she studied plants by getting to know them as individuals and 
cells by getting inside them than for the important genetic discov- 
eries she made. The image of McClintock shrinking into the cell 
has a vividness that conveys a certain sense of an anti-abstract 
approach, but to appreciate the point in more than a superficial 
way, you should read Keller's book or look for new additions to 
the burgeoning field of criticism of traditional epistemology. 

It might be more accurate to describe the blind spot I attributed 
to Piaget and Levi-Strauss as "resistance," in the sense that Freud 
uses when he explains reluctance to accept his theories as a 
manifestation of what the theory predicts — a repression of the 
unacceptable aggressive or sexual content of the unconscious. In 
Piaget's case the unacceptable is the possibility that good thinking 
might not conform to the standards that have been set up by 
generations of epistemologists. The repression consists of accept- 
ing the existence and effectiveness of such thinking but relegating 
it to children. Readers who have battled with Piaget's writing 
might even go a step further with me in speculating that Piaget is 
protecting himself from acknowledging that his own thinking has 
more of the bricoleur than of the formal and analytic standards of 
the dominant epistemology. But whatever the ultimate reason, the 
fact is that Piaget hid the light of his best discovery under' the 
bushel of his theory of stages. 

In outline, Piaget's theory presents intellectual development as 
divided into three great epochs, which (by coincidence or other- 
wise) approximately match three major periods in the timetable of 
life as seen by School. The first epoch, called the "sensorimotor 
stage," is roughly the same as the preschool period. This is a 
period of prelogic in which children respond to their immediate 

Instructionism versus Constructionism • 153 

situation. The second epoch, which Piaget calls the stage of "con- 
crete operations," is roughly coextensive with the elementary- 
school years. This is a period of concrete logic in which thought 
goes far beyond the immediate situation but still does not work 
through the operation of universal principles. Instead, its methods 
are still tied to specific situations, like those of an expert at kitchen 
math who is incapable of handling a pencil-and-paper test on 
fractions. And finally there is the "formal stage," which covers 
high school — and the rest of life. Now at last thought is driven, 
and disciplined, by principles of logic, by deduction, by induction, 
and by the principle of developing theories by the test of empirical 
verification and refutation. 

This neat picture of successive stages has aroused such strong 
positive and negative reactions that the ensuing debates have 
obscured Piaget's really important contribution: His description of 
different ways of knowing is far more important than quibbling 
about whether they neatly follow one another chronologically. 
And what is especially important is the description of the nature 
and the development of the middle stage of concrete operations. 
This is the task to which he devoted the greater part of his mature 
life and the topic of all but a handful of the more than one 
hundred books he wrote about how children think in a staggering 
range of domains, including logic, number, space, time, motion, 
life, causality, machines, games, dreams. 

5 Piaget's descriptions of thousands of conversations with chil- 
dren fit well with Levi-Strauss's image of the bricoleur. The child 
will bring to bear on a situation a way of thinking about it that 
might be very different from what is used in a seemingly logically 
equivalent problem. Where Piaget has something very different to 
add is in his focus on change over periods of years. For example, 
;he has conversations with children as young as four about situa- 
tions involving number. 

The best-known examples are the so-called conservation ex- 
periments. In one of these, children whose ages vary from four to 
seven are shown a row of egg cups, each containing an egg, and 

154 . The Children's Machine 

a* asked whether there are more egg, or more egg cups The 

then reSP °r: 31 311 agCS iS " n °" or " the The 

then removed from the egg cups and spread out in a lonfr™ 

view or the child. The same question is posed. This has been done 

ateX^' " SUffidently Varied -ndiUonsXX 

Xv C ^ **** aU children of four or five 

Wdl Say more e ^ s " They will defend this position under exten 
-e xros s-questioning and even when pressure is placed on Z m 

^T*nZT s ' for exampIe ' by ^ told ^ oZ 


able obZll " S ^ e88S " Thus the fi «" -mark- 

able observation from the experiment is that these children seem 

Zd h^f o ' S ° ° bViOUS th3t nobod y see ™ to have no- 

Zt T^r ** Children did n0t Share our self-TLent 

*u* The pomt is not simply that the children do not know the 

ZS m ZV^ T Sti ° n ^ fl ° Under in ^-e ; " 
that they firmly and consistently give a different answer 

l^ZT^ ^ ^ »** °" What is being 
ion- ThPv »hi n L- ,k , nonconservationist" opin- 

rrue If rh.^h L „ ° ne Mnse objection must be 

trivializes Piaget's exLlen ™her than 

standi™ bur it L & ™ Y mdeed De a misunder- 

standing, but it is not a "mere verbal misunderstanding » It reflects 
something deep about the child's mental world. U one sus^ 

number, not space. However, saying this to a four-vear-old will 
CUOn - NUmber 1S What s - on "Sesame Street/' and space 

Instructionism versus Constructionism • 155 

is where you sit. Neither is relevant to the distinction about eggs 
and egg cups. The possibility of the misunderstanding shows the 
state of development of this area of a child's knowledge. The work 
being done in the concrete period is that of gradually growing the 
relevant mental entities and giving them connections so that such 
distinctions become meaningful. When you or I see six eggs, the 
sixness is as much pan of what we see as the whiteness or the 
shapes of the individual objects. As with Debbie, for us number 
(like fractions) is something we "put on" everything. But we must 
"have" it before we can do so, and it seems that for a sensorimotor 
child it is either not there or, like the early Debbie's fractions, too 
rigidly anchored to be manipulated. Following this thought, I see 
phenomena that Piaget ascribes to the stage of concrete opera- 
tions as models for how fractions developed for Debbie or how 
"flowerness" and "familyness" (in the botanical sense) developed 
for me. In this view the educational implications of Piaget's ideas 
are reversed. Most of his followers in education set out to hasten 
(or at least consolidate) the passage of the child beyond concrete 
operations. My strategy is to strengthen and perpetuate the typical 
concrete process even at my age. Rather than pushing children to 
think like adults, we might do better to remember that they are 
great learners and to try harder to be more like them. While formal 
thinking may be able to do much that is beyond the scope of 
concrete methods, the concrete processes have their own power. 

It is impossible not to feel frustrated in thinking about the 
nature of concrete knowledge by the advantages enjoyed by the 
traditional epistemology. Its unit of knowledge is a clearly demar- 
cated entity — a proposition-— and there is a well-developed, 
widely accepted language in which to talk about it. Part of the gap 
one encounters in developing any alternative epistemology is the 
result of time: Starting fresh, we are essentially at a disadvantage. 
Part of the gap is very likely to be permanent, for an epistemology 
Predicated on pluralism and on connection between domains is 
bound to be less clear-cut, more complex. 

A third kind of gap, which is of a more subtle nature, is the 

156 • The Children's Machine 

relationship of knowledge to media. The traditional epistemology 
is based on the proposition, so closely linked to the medium of 
text — written and especially printed. Bricolage and concrete 
thinking always existed but were marginalized in scholarly con- 
texts by the privileged position of text. As we move into the 
computer age and new and more dynamic media emerge, this will 
change. Although it might be futile to outguess such radical depar- 
tures in ways of dealing with knowledge, it will be interesting to 
keep the question in mind as we turn now to look more directly 
at some aspects of the history of computers in relation to episte- 
mology and learning. 


THE pioneers who made the first computers knew exactly 
what kind of work the machines would do and what style 
of mind they would serve. It was the 1940s. The world was 
at war. Complex calculations had to be done under time pressures 
not normally felt by mathematicians: numerical calculations re- 
lated to the design and use of weapons; logical manipulations to 
break ever more complex codes before the information became 
old news. The pioneers were mathematicians and built the ma- 
chines in their own image. It is unlikely that they gave even a 
passing thought to making computers user-friendly to people with 
softer styles than theirs. The conditions were set for the develop- 
ment of a computer culture with no room for pluralism; its episte- 
mological norms would be firmly planted in the most analytic 
tradition. It was inevitably a culture of "hards." 

Wartime conditions were not the only factor shaping the com- 
puter culture in this way. The stage of development of the technol- 
ogy acted in the same direction. The very appearance of the early 
machines would strike terror into the technologically faint of 
heart. The first one I saw (the British ACE designed by Alan Turing 
himself) looked less like a machine than a robots' library with 

154 • The Children's Machine 

are asted whether there are more eggs or more egg cups. The 
typical response at all ages is "no" or "the same." The eggs are 
then removed from the egg cups and spread out in a lolfrow 

^ITtT brought together in a tight cluster - ** «* 

view ot the child. The same quesuon is posed. This has been done 
often enough, and under sufficiently varied conditions, to justify 

will say more eggs." They will defend this position under exten- 
«ve xross -questioning and even when pressure is placed on them 
to change tor rninds, for example, by being told that three othe" 
children all said there were not more eggs, or by beine asked to 
count the eggs and the egg cups. Most^clren'wS S^ 
m hne Wlt h the others, and one neady commented after count!^ 
They count the same but it's more eggs." Thus the first remal 
to hoti r 3000 fr ° m eXPedment is that ^ildren seem 

J a irZTT* t0 K Something that is abso,utel y <° 

TJt. ^ d ' S ° ° bViOUS that nobod y see ™ to have no- 
oced before Ptaget that children did not share our self-evident 

alt antT? *** *" the Children do ™ ^ow the 

^1 t Z e filt 6 T Sti ° n ^ fl ° Under ^ the P** 

, *«J fin"* and consistently give a different answer 

A sensible objection that casts light on what is really being 

teamed is that the children are more likely to have misunderstood 

ton rZ Z Tu t0 h ° ld ^ ^ "conservationist" opin- 
>oa They think they are being asked about the space occupied 

true If the children really understood the question as we do they 

rnd^ h,^ eXPe " ment - There ind <* d be a misunder- 
standing, but it is not a "mere verbal misunderstanding » It reflects 
something deep about the child's mental world. If one su^S 
an adult of such misunderstanding, one would say, "No 1^ 

oT T H r VCri S3ying to a f--yel,d 

ZLtL P 7° S K ° r ^ CMd dOCS n0t know h ™ to make the 
distinction. Number is what you see on "Sesame Street," and space 

Instructionism versus Constructionism • 155 

is where you sit. Neither is relevant to the distinction about eggs 
and egg cups. The possibility of the misunderstanding shows the 
state of development of this area of a child's knowledge. The work 
being done in the concrete period is that of gradually growing the 
relevant mental entities and giving them connections so that such 
distinctions become meaningful. When you or I see six eggs, the 
sixness is as much part of what we see as the whiteness or the 
shapes of the individual objects. As with Debbie, for us number 
(like fractions) is something we "put on" everything. But we must 
"have" it before we can do so, and it seems that for a sensorimotor 
child it is either not there or, like the early Debbie's fractions, too 
rigidly anchored to be manipulated. Following this thought, I see 
phenomena that Piaget ascribes to the stage of concrete opera- 
tions as models for how fractions developed for Debbie or how 
"flowerness" and "familyness" (in the botanical sense) developed 
for me. In this view the educational implications of Piaget's ideas 
are reversed. Most of his followers in education set out to hasten 
(or at least consolidate) the passage of the child beyond concrete 
operations. My strategy is to strengthen and perpetuate the typical 
concrete process even at my age. Rather than pushing children to 
think like adults, we might do better to remember that they are 
great learners and to try harder to be more like them. While formal 
thinking may be able to do much that is beyond the scope of 
concrete methods, the concrete processes have their own power. 
It is impossible not to feel frustrated in thinking about the 
nature of concrete knowledge by the advantages enjoyed by the 
traditional epistemology. Its unit of knowledge is a clearly demar- 
cated entity — a proposition — and there is a well-developed, 
widely accepted language in which to talk about it. Pan of the gap 
one encounters in developing any alternative epistemology is the 
result of time: Starting fresh, we are essentially at a disadvantage. 
*art of the gap is very likely to be permanent, for an epistemology 
Predicated on pluralism and on connection between domains is 
bound to be less clear-cut, more complex. 

A third kind of gap, which is of a more subtle nature, is the 

156 • The Children's Machine 

relationship of knowledge to media. The traditional epistemology 
is based on the proposition, so closely linked to the medium of 
text—written and especially printed, Bricolage and concrete 
thinking always existed but were marginalized in scholarly con- 
texts by the privileged position of text. As we move into the 
computer age and new and more dynamic media emerge, this will 
change. Although it might be futile to outguess such radical depar- 
tures in ways of dealing with knowledge, it will be interesting to 
keep the question in mind as we turn now to look more directly 
at some aspects of the history of computers in relation to episte- 
mology and learning. 



THE pioneers who made the first computers knew exactly 
what kind of work the machines would do and what style 
of mind they would serve. It was the 1940s. The world was 
at war. Complex calculations had to be done under time pressures 
not normally felt by mathematicians: numerical calculations re- 
lated to the design and use of weapons; logical manipulations to 
break ever more complex codes before the information became 
old news. The pioneers were mathematicians and built the ma- 
chines in their own image. It is unlikely that they gave even a 
passing thought to making computers user-friendly to people with 
softer styles than theirs. The conditions were set for the develop- 
ment of a computer culture with no room for pluralism; its episte- 
mological norms would be firmly planted in the most analytic 
tradition. It was inevitably a culture of "hards." 

Wartime conditions were not the only factor shaping the com- 
puter culture in this way. The stage of development of the technol- 
ogy acted in the same direction. The very appearance of the early 
machines would strike terror into the technologically faint of 
heart. The first one I saw (the British ACE designed by Alan Turing 
himself) looked less like a machine than a robots' library with 

158 • The Children's Machine 

racks of electronics in place of books. No way of using it would 
have made it congenial to a technophobic teacher tentatively 
exploring her first relationship with a machine! In addition to their 
appearance, the technical weakness of the machines contributed 
to forcing a very hard-edged way of using them. Interfaces like 
those that make today's computers more "friendly" require lots of 
surplus computer power. In those days one always had to 
squeeze the last ounce of power from the machine to get even the 
simplest jobs done, and this often meant carrying out contortions 
of mathematical computation in one's own mind. I remember my 
first experiences of programming as being much more like solving 
problems in number theory than the self-expressive activity I as- 
cribed to Debbie or Brian or the Costa Rican teachers. The point 
I am making is not simply that this was a mathematical culture 
Cwhich it was), but that it was the particular kind of mathematical 
culture in which precise calculation plays the dominant role and 
the technical and analytic have more weight than the intuitive and 
the experiential. 

Thus, many factors conspired to cast the early computer culture 
in the hard and analytic shape that for most people remains even 
today synonymous with the word computer. After the war the 
computer slowly moved out of the sanctums of high science and 
the military into a wider world of business and run-of-the-mill 
industrial and university research. As it did so it took its culture 
with it, and so the popular image of the computer as "analytical 
logic engine" grew up and took root. What is significant here is 
how elements of the original computer culture persisted even 
when the technology no longer required or favored them. Once 
launched, the culture acquires a logic of its own. Although some 
of the mathematical extremes of the early ways to control comput- 
ers were gradually softened, the hard core remained. 

When I programmed the ACE I actually had to express instruc- 
tions as sequences of Os and Is coded by literally punching holes 
one by one in an IBM card. I do not remember the code, but 
similar codes still exist for modern machines: For example, the 

Computerists • 159 

sequence 1 10000101 1101011 10000010001 1 100 could be an instruc- 
tion to the central processor to add the numbers in two given 
memory positions. But although these codes still have theoretical 
importance, someone writing a program today rarely uses them as 
the actual medium of expression. 

Expressing instructions as binary numbers is too opaque and 
tedious even for a mathematician to find comfortable. It did not 
take long before computer languages were developed to allow an 
, instruction to be expressed in a form more like z = x +y, to mean 
that the numbers in the memory positions x and y are added 
together and the result placed in memory location z. One of the 
intellectually powerful facts about computers is that they can ma- 
nipulate their own programs: Since the computer can be pro- 
grammed to translate z = x+y into the appropriate binary num- 
ber, the only time it is absolutely necessary to use the binary code 
is to write the program that does the translation. 

The development of more transparent and congenial forms of 
expression did not mean an end to the hard-edged analytic style 
of thinking in programming; it only softened its most obtrusive 
manifestations. The mark of the mathematician was still there in 
•the algebraic form of the instruction, and it was stamped on the 
^Culture of programming in deeper ways than this. As one might 
have expected, it was mathematicians with a hard-edged bent of 
|mind who were most inclined to create theories of the proper 
iistructure of a computer program and make the effort to set up 
|^tandards for the process of writing one. The result was to consoli- 
§date their view of programming as the only right one. Thus a new 
pind of factor became visible, which still buttresses the hard- 
edged computer culture today. The hards have an advantage in 
the ability and desire to offer theoretical justifications for their 
Ways of doing things. A similar self-perpetuating factor works 
through the recruitment of people. The dominance of the hard- 
edged style in the culture draws new recruits who think in that 
w ay, and discourages those who would tend to push its develop- 
ptent in another, softer direction. 

160 • The Children's Machine 

As the computer spread to wider worlds of application, the idea 
of using it in education was bound to come up. Indeed, by the 
early 1960s an unfamiliar set of actors had become visible on the 
fringes of the education scene. The technology we brought with 
us (for I was one of these computerists attracted by the prospect 
of change in education) was extraordinarily primitive. A typical 
project of the time would sit a child in front of a clattering teletype 
machine connected with a distant computer that was too big and 
expensive to bring to the child. There was none of the graphics, 
the color, the action, and the sounds that contribute to the excite- 
ment of the computers children know and love today. Very little 
of what was actually done or learned under such circumstances is 
directly applicable today. But in contrast with the ephemerality of 
the technological forms of those days stands the resilience of the 
theoretical orientations — the ideologies — we brought with us 
from the larger computer culture. 

The important and lasting side of what we did was planting the 
seed of a specifically educational computer culture. The theme of 
this chapter is the development of this seed into a tree with so 
many branches that I shall have to be selective in discussing them. 
In selecting the branches that seem most important I have concen- 
trated on those in which I have been most active. I hope this is not 
because I see importance only where I have worked; I prefer to 
believe that this is because I have tried to work in the areas that 
are most important. 

The easiest way to tell the history of the educational computer is 
quantitative. In the 1960s we were a small handful, mostly of 
academics who had strayed in from other fields: for example, 
Patrick Suppes from philosophy and psychology, John Kemeny 
(who invented basic) from physics and university administration, 
Donald Bitzer (who developed the plato system) from engineer- 
ing, and myself from mathematics and the study of intelligence. 
There were also a few entrepreneurs who lost money in prema- 
ture attempts to commercialize the field. In the early 1970s we 

Computerists • 161 

were a larger handful. The big break came with the advent of the 
microcomputer in the middle of the decade. By the early 1980s the 
numbers of people who devoted a significant part of their profes- 
sional time to computers and education had shot up from a few 
hundred to tens of thousands. By now it is in the hundreds of 
thousands, most of them teachers, although many thousands are 
engaged in the research and business wings of the world of edu- 
cational computing. 

The story that is harder to tell but also far more important to 
know is subjective and sociological. It concerns what these grow- 
ing numbers of people think and how the development of this 
culture relates to wider trends in society. My overarching message 
to anyone who wishes to influence, or simply understand, the 
development of educational computing is that it is not about one 
damn product after another (to paraphrase a saying about how 
school teaches history). Its essence is the growth of a culture, and 
it can be influenced constructively only through understanding 
and fostering trends in this culture. 

The first significant move toward taking understanding beyond 
a quantitative level was the attempt to classify the modes of use of 
computers in education. The title of one of the first anthologies of 
papers in the area provides a witty formulation that illustrates the 
approach. The book by Robert Taylor (professor at Columbia 
Teachers College and creator of the first Master's program in com- 
puters and education) was called The Computer in the School: 
TUtor, Tutee, Tool. The intention of the first and last terms of the 
subtitle corresponds closely enough to popular models of what 
computers can do in education. Examples of the uses of comput- 
ers considered as tools will be familiar to everyone. A word 
processor is considered to be a tool; so is a program that allows 
one to study ecology through simulations; and so are programs 
that allow one to use the computer as a calculator. The term tutor 
names the most common image of the computer in education. 
The term tutee, on the other hand, refers to a metaphor I have 
frequently used in thinking about programming as teaching the 

162 • The Children's Machine 

computer Every professor knows ,ha, a good way ,o learn a 
ub,ea . by reaching a course on it, and , half playful lusted 
har a ch d could ge, some of ,he same kind «* bS£5£ 
■ng, '"aits to say, programming, the computer 
used thf """"""I daSSificato " ** has been so frequendy 
ab« L„ ""LT " ab ' C '° iden, "V '« author tali 

and Tea STL" ^ """^ *™» computer 

and learmng about the computer." With corresponds neadv m 

'» less direct but still exists, in that being able to program a 
puter ,s synonymoua ^ leaming ^ 

works than ,s required by the other two modes of use 

In thts chapter, however, instead of classifying ways of usins 
computers, I look at the development of wa™ of ZL K 8 

ZZS-ttZLr ~,"burt: f 

a Zld nf rh ^ ' ^ and Cridcal stand ^s that were 

rh!r f "nnugrants, we structured our work in wavs 

lVJT Y c ^ ettg T ho ^ fundamental -~ EvZ 

Schoolish mofd 7 1 1 566 n ° W as a --emarkably 

ctaTctLcs t IO C ° minUe d ° W " Webster's list of 

characters, was certamly controlled; indeed, it was not even 

Computerists • 163 

acknowledged as a relevant category for tninking about educa- 
tion. The prevailing computer culture favored keeping our focus 
firmly on the cognitive side of education. 

A look at three participants in the early educational computer 
culture, Suppes, Kemeny, and myself, will be sufficient to show 
how its "classicism" cuts across ideas and debates about modes 
of use of computers in education. Patrick Suppes became the 
intellectual father of CAI (Computer Aided Instruction), a phrase 
that has become synonymous with the mode of use of the com- 
puter I characterized with some polemical overstatement as 
using the computer to program the student. John Kemeny was 
one of the fathers of basic and therefore a pillar of support for a 
very different view of the computer: The student programs the 
computer and so makes it a tool that aids learning rather than a 
robot teacher that aids instruction. Thus, along one axis Suppes 
and Kemeny stood at opposite extremes. But on other relevant 
axes they were very close. They shared a virtually exclusive em- 
phasis on the cognitive side of learning: They saw learning in 
terms of facts and skills to be acquired; they had no explicit 
concern for feelings or for personality or for development of 
the individual on a level that was not reducible to such spe- 
cific atoms of learning. They shared an acceptance of School. 
They kept their views on education separate from their engage- 
ment with politics, gender, and race. In many such respects they 
were distinct from the spirit of the "romantic" period, which 
would bring hotter social issues and more "intimate" aspects 
of the computer to the forefront of concern. And so, on the 
whole, was I. 

I was certainly the obstreperous maverick of the group. I quar- 
reled with both CAI and basic and developed Logo as an alterna- 
tive to both. But it would take me five years to understand the 
anticlassical implications of ideas with which I was grappling. In 
the meantime I found myself acting like a "person of my time" (or 
perhaps even like a "man of my time" — my own work has only 
gradually broken with what I recognize as androcentrism, and 

164 • The Children's Machine 

some of my feminist friends would deny that a male could ever 
completely break with it). 

The concept of CAI, for which Suppes's original work was the 
seminal model, has been criticized as using the computer as an 
expensive set of flash cards. Nothing could be further from 
Suppes's intention than any idea of mere repetitive rote. His theo- 
retical approach had persuaded him that a correct theory of learn- 
ing would allow the computer to generate, in a way that no set of 
flash cards could imitate, an optimal sequence of presentations 
based on the past history of the individual learner. At the same 
time the children's responses would provide significant data for 
the further development of the theory of learning. This was seri- 
ous high science. 

However, from the beginning several considerations kept the 
approach from sitting well with me. 

My gut-level response rejected the status of object given to the 
child by any theory of this kind. Behaviorists are fond of using the 
designation "learning theory" for the foundations of their think- 
ing, but what they are talking about is not "learning" in the sense 
of something a learner does but "instruction," in the sense of 
something the instructor does to the learner. 

The form in which I was best able to articulate my disagreement 
at that time was epistemological, that is to say, in terms of differ- 
ences about the kinds of knowledge being used. Suppes's instruc- 
tional theory sought to reduce what children needed to learn in 
mathematics to a set of precise "factlets" that could be counted 
and sequenced by his computer programs. In this he was not 
being idiosyncratic. The logician in him supported a view of 
knowledge as made up of precise particles; the statistician in him 
liked to see knowledge as particulate and therefore countable; the 
neobehaviorist required it to be so. What was expressed in his 
work was an all-embracing epistemological paradigm, which was 
then dominant in large sectors (and is still powerful in some 
sectors) of the American academic world. From my side too this, 
paradigm was very present in the theoretical worlds from which 

Computerists • 165 

I came to educational endeavors — but as an obstacle to be chal- 
lenged. In psychology my mentor Piaget was the most consistent 
(though in America Noam Chomksy had become known as the 
most vehement) critic of behaviorism. In artificial intelligence (AI), 
my work with Marvin Minsky struggled against "logic" as the basis 
of reasoning and against all forms of "particulate" and "proposi- 
tional" representations of knowledge. 

The issue comes out in a stark form by contrasting two views 
of Debbie. CAI is based on a diagnosis of Debbie's difficulty as a 
deficiency of specific items of knowledge about fractions and 
seeks to cure the problem by supplying them. I see a defi- 
ciency — or even multiple deficiencies— in relationship; There is 
debilitating weakness both in Debbie's own relationship with 
fractions and in the relationships among the different pockets of 
what knowledge she does have. As a result she is unable to take 
charge either of making effective use of her existing knowledge or 
of generating or seeking new knowledge. I pose the educational 
goal not as giving her factlets but as encouraging her to make 
connections between different elements of what she already 
knows: for example, intuitive knowledge about fractions, knowl- 
edge about the "real world," and knowledge about strategies of 
learning. Making the connections is something only Debbie can 
do. They have to be her connections. 

The advocate of CAI might say, "But we have seen that if you 
put people like Debbie through our programs their scores will 
improve. The approach must be right." Perhaps her scores will 
improve, but it does not follow that the underlying theory is right. 
The question always arises: Is there another, equally likely expla- 
nation? An anecdote points to one. 

I was observing a child working with a CAI program for multi- 
plication. There was something strange going on. I had seen the 
child do several multiplications quickly and accurately. Then I saw 
him give a series of wrong answers to easier problems. It took me 
a while to realize that the child had become bored with the 
program and was having a better time playing a game of his own 

166 • The Children's Machine 

invention. The game required some thinking. It redefined the 
"correct" answer to the computer's questions as the answer that 
would generate the most computer activity when the program 
spewed out explanations of the "mistake." 

I would bet this child was one of those who would become a 
statistic showing gain in math ability from the use of the CAI 
program. Would it follow that the program was in fact a good way 
to teach math? Yes and no! Yes, because it did, in fact, enable the 
child to learn; no, because it did so for a reason quite different, 
from what the programmer intended. The issue at stake here is 
whether self-directed activity was better than carefully controlled 
programmed activity for learning math, and this child supported 
the self-directed alternative. A CAI salesperson might still object 
(though I am sure Suppes would not) that this is of no importance 
if the child did in fact learn. My reply to that is what I say about 
most learning by rote methods with or without computers: Yes, 
indeed, children can make a game of anything and learn through 
it, but if that's what we want to see happen let's say so and work 
hard to find contexts in which playfulness is brought out to best 

The anecdote illustrates the difference between the intellectual 
atmosphere of Suppes's background and mine. While he was 
working in the tighdy controlled thinking of logic, I was working 
in the playful atmosphere of the MIT AI Lab. Of course, neither of 
us denied the importance of both formal and intuitive thinking. 
But we saw a reversal of relationship between them. The logician 
sees logic as the primary kind of thinking and struggles to explain 
the intuitive in logical terms. Many of my colleagues in artificial 
intelligence argued (and some still do) that when we are doing 
what we think of as intuitive thought, we are still following (with- 
out knowing it) precise, logical rules— only they are not the rules 
we might think that we are following. This is why they are de- 
lighted whenever anyone programs a computer to do something 
that resembles intuitive reasoning. The computer is following 
definite rules, so the task, whatever it is, can be done by following 

Computerists • 167 

1. rules. For me the challenge is in the other sense. The basic kind 
I of thought is intuitive; formal logical thinking is an artificial, 
§. though certainly often enormously useful, construct: Logic is on 
: tap, not on top. I am delighted whenever something that appeared 
I to be formal, rule-driven behavior turns out to be something else. 

This is why I was so pleased with the child playing with the CAI 


m Thus Suppes and I differed quite deeply about what kind of 
I knowledge we wanted to foster in children. A mark of authenticity 
1 in our debate is that we differed also in our own personal styles — 
|| both in how we thought and in our appreciations of how we 

p In one of my first encounters with Suppes he had formulated 
i the issue of styles by summing up a debate between us at a 
| conference on the philosophy of science. I remember his words 
g well, since they came to be emblematic for me of what I often saw 
||as the fundamental problem of teaching: "I would rather be pre- 
§|cisely wrong than vaguely right." 

g I saw this as a fundamental problem for teaching in this sense. 
| It had been obvious to me for a long time that one of the major 
^difficulties in school subjects such as mathematics and science is 
that School insists on the student being precisely right. Surely it is 
-necessary in some situations to be precisely right. But these situa- 
tions cannot be the right ones for developing the kind of thinking 
jihat I most treasure in myself and many creative people I know, 
fciis is not thinking that goes as the logician might like, from truth 
jo truth to truth until it gets from premise to solution. The normal 
■ State of thinking is to be off course all the time and make correc- 
tions that go back sufficiently to keep going in a generally good 
|p!irection. This kind of thinking is always vaguely right and 
vaguely wrong at the same time. 
M The teaching dilemma comes from the difficulty in knowing 
pwhere someone else is in such a process. So how can the teacher 
jpive advice to the student? 

P I had devoted much effort to looking for a theory of how 

168 • The Children's Machine 

teachers could do this. I now see that I had not been able to find 
anything very deep for reasons rather like those that blocked the 
teacher at my Logo workshop.- 1 was fixated on children in School 
and so was looking for ways to improve the guidance process i n 
traditional schoolwork. The breakthrough that set me on track to 
what would become my trademark way of using computers came 
when I was able to "forget the childrer ,. and think ab( J 

It happened on a visit to Cyprus in 1965. 1 was still reeling from 
the culture shock that came with moving (in 1963) from the Uni- 
versity of Geneva, where there were no computers, to MIT, where 
I suddenly had free access to the best machines in the world Here 
on this remote Mediterranean island I was feeling my first absence 
from a way of life in which computers were a constant presence 
This in turn stirred up thoughts about how much I had learned 
since coming to MIT, how I had used a computer to make a 
breakthrough on a theoretical problem that had bothered me for 
some time, how concepts related to computers were changing my 
thinking in many different areas. Then in a flash came the "obvi- 
ous idea: What computers had offered me was exactly what they 
should offer children! They should serve children as instruments 
to work with and to think with, as the means to carry out projects, 
the source of concepts to think new ideas. The last thing in the 
world I wanted or needed was a drill and practice program telling 
me to do this sum next or spell that word! Why should we impose 
such a thing on children? What had launched me into a new spurt 
of personal learning at MIT wasn't in the slightest bit like the CAI 
programs. I became obsessed with the question, Could access to 
computers allow children something like the kind of intellectual 
boost I felt I had gained from access to computers at MTP 

In a search for good examples of what children might actually 
do with computers, my mind raced through my own activities, 
making lists of ways in which I thought I had benefited from 
computers and asking myself in each case whether something 
similar could be made available for children. For a while I simply 

Computertsts • 169 

passed over the first entry on my list: artificial intelligence, the 
principal interest that had brought me to MIT. "Obviously not for 
children." Then I remembered a conversation with Piaget a few 
years before in which we had engaged in playful speculation 
about what would happen if children could play at building little 
artificial minds. I had been saying that the essence of AI was to 
make theoretical psychology concrete. So (since concreteness is 
supposedly what children thrive on) in principle perhaps some 
elementary form of it could become a children's construction set. 
If psychologists could benefit from making concrete models of the 
mind, why shouldn't children, whose need was even greater, also 

Piaget liked the image of taking one of his favorite apho- 
risms — "to understand is to invent" — into a new domain. In the 
hothouse atmosphere of the discussion in Piaget's incredibly cha- 
otic study, we were carried away by images of children under- 
standing thinking through playing with materials needed to invent 
a thinking machine, an intelligence. Neither of us thought of it as 
very real — it was just a scenario for a philosophical Gedankenex- 
periment. But now suddenly on a mountain in Cyprus, the idea 
changed for me from a philosophical speculation to a real project. 

The difference came from a very concrete picture of (one ver- 
sion of) what people actually do when they "do AI." They select 
a piece of human mental activity, say, playing chess or seeing a cat; 
then they write a computer program that will do something simi- 
lar; and finally they discuss, sometimes at very great length, 
whether the computer program "really" does what the human did. 
I had been engaged in a lot of this kind of activity and knew it had 
stimulated me to exciting and productive insights into human 
thinking. True, I did not often really think that the AI program was 
successful in fully imitating a person; but even when the diifer- 
ences were more prominent than the similarities, the discussion of 
the machine still produced valuable insights into how people 
think — and into how they do not think. It seemed plausible that 
doing elementary AI could give children, too, a new context for 

170 • The Children's Machine 

thinking about thinking. Of course I would not expect them to be 
able to make a program to play even poor chess, so I cast around 
for a simpler game and fixed on something in the family of games 
played with piles of matchsticks. The principle, however, could be 
the same. My hopeful scenario of children doing elementary AI 
was something as follows. 

A group of children is studying the matchstick game called 
"Twenty-one," in which two players take turns in removing one, 
two, or three matches from a pile of twenty-one matches; the one 
who takes the last match loses. The children's immediate goal is 
exactly that of people making what would later come to be called 
expert systems: Carefully watch someone engaged in the activity 
you want your program to imitate, and try to come up with rules 
you can put into a program to make the computer act similarly. 
The physical side of the process did not seem important. Today 
the means exist for children to build a robot that would play by 
actually picking up sticks. I actually built one for relaxation (and 
because I like that kind of joke) while writing this chapter, using 
an extended Lego kit called Lego-Logo, which was a fallout 
(twenty years later!) of the very work I am describing here. In 
state-of-the-art present-day educational computing, the game 
would be played using computational objects visible as icons on 
a screen — the computer would play by moving the icon from the 
row into a bin and the human opponent by dragging it with a 
mouse or by using keys. Back in the 1960s we used clattering 
teletype machines; when we got the scenario to work, the matches 
were X's and the machine retyped the row after each move. The 
human player responded by typing a number. What seemed im- 
portant was how the children would do the programming and, 
indeed, whether the idea ran counter to established knowledge 
on stages of intellectual development. 

My friends in the developmental psychology business were 
cynical about whether anything that could significantly be called 
programming could be managed by children who had not yet 
reached the so-called formal stage of development, which means 

Computerists • 171 

about junior high school age. I saw the question as more subtle 
because I was more aware of how much it would depend on 
what is meant by "programming." It seemed intuitively obvious 
that nothing good would come of trying to have third-graders or 
even fifth-graders make game-playing programs from scratch in 
any of the then current programming languages such as Fortran 
or usp. (Had basic or pascal existed I would have included them 
as well.) But was this because the languages were designed for 
adults and presupposed some elements of mathematical sophis- 
tication, or was it inherent in the concept of programming? In- 
deed, is there such a thing as "the concept of programming," or 
is "programming" something that can be constructed in radically 
different ways? 

One could go around in circles forever with such questions. 
The only sensible approach was to take a first shot at making a 
programming language that had a better chance of matching the 
needs and capabilities of younger people than the existing ones. 
At the time, while working at MIT, I was also doing some part-time 
consulting for a group led by Wally Feverzeig, head of educational 
technology at the research firm Bolt, Beranek, and Newman, 
which was working on one of the earliest attempts to teach pro- 
gramming in a school. The group did not need much persuasion 
to change its goal from trying to teach existing programming 
languages to developing an entirely new language. We formed a 
team, and the next year the first language bearing the name Logo 
was up and running — though few of the million or so children 
who work with a modern form of Logo on any school day would 
recognize it. We decided that it was prudent to make the first trial 
at the junior high level just inside the "formal" boundary; the idea 
was to descend to lower ages as we developed techniques for 
teaching and improvements to the language. 

It took two years and a lot of work to get from Cyprus to a place 
where young people (seventh-graders) could actually do some- 
thing like the scenario. Not only did they do so, they even pro- 
duced an unexpected twist that made the reality more interesting 

172 • The Children's Machine 

than the fantasy. Rather than follow strictly in the path of the 
so-called "knowledge engineers" who build expert systems, these 
students followed in the path of psychologists who deliberately 
construct a series of "inexpert" systems that make the computer 
act like a "novice" and then pass through a progression of levels 
of increasing expertise. 

Unsurprisingly (in hindsight!) our young students were more 
intrigued by what some of them called "dumb programs" than 
by "smart programs." It might be fun to make a program that 
would play impeccably and always win, but some found it more 
enjoyable to make one they could beat and laugh at for commit- 
ting the blunders they saw their friends make. The real case ex- 
ceeded my original fantasy scenario in giving rise to good talk 
about much more than computers and programming. In one 
class the use of the words dumb and smart became a subject of 
intense discussion triggered by an interchange in which A said 
B's program was dumb and B countered with something like: 
"It's not dumb, I did it specially like that so I could add more 
rules. Wait and see, it'll be the smartest! Real dumb is when you 
make it so you can't add anything, it can't get better." In another 
class, discussion led to arguments about whether these judg- 
mental words should be applied to the program or to the pro- 
grammer and ended up with a consensus: Using words like 
dumb and smart is what's really dumb. 

B reminded me of Patrick Suppes's comment about being 
vaguely right or precisely wrong, by defending a strategy of delib- 
erately designing a program that would be only vaguely right but 
capable of being redirected, instead of shooting for being pre- 
cisely right on the first shot and risking a complete miss. In this he 
expressed the same thought that underlies Voltaire's maxim, "the 
best is the enemy of the good," which Herbert Simon, Nobel 
Prize-winning economist and one of the founders of AI, takes as 
his life motto. All three thinkers, Voltaire, Simon, and B, suggest 
a slant on what is really wrong with School's epistemology: the 
very little room it leaves for being vaguely right. 

Computerists • 173 

It is not merely an intolerant style of teaching or testing that is 
responsible for the insistence in so much of schoolwork on being 
exactly right. The content of the curriculum and the medium of 
pencil and paper are inherently biased toward a true/false-right/ 
wrong epistemology. What B discovered was that programming is 
inherently biased toward evaluation not by "is it right?" but by 
"where can it go from here?" In this he is not alone: Many virtuoso 
programmers insist on starting a job by making a "quick and dirty- 
program that is vaguely what is wanted and then seeing how to 
go from there. Of course, the same is true in other (perhaps all) 
domains of creative work. My interpretation of such stories as B's 
will be that while he could have made this discovery in other 
domains (obviously!— many did so before computers came on 
the scene), programming in the right supportive context offers 
especially favorable conditions, and the more so the younger the 

The game of Twenty-one turned out to be simple enough to be 
played by programs within the grasp of seventh-graders who were 
indeed able to draw on the experience for discussion of strategies 
for thinking. Students took with gusto to making programs that 
would generate sentences in approximate English and through 
doing so came to a new kind of understanding of grammar. But 
something was missing, and the idea of children doing AI did not 
really take off until we married it, nearly twenty years later, with 
Lego to produce a construction set for building programmable 
robots. The difference between these two situations touches the 
heart of my story, indeed of this whole book. But I am getting 

ahead of myself. 

At the time I was both happy and frustrated. The experiment 
showed that seventh-graders could learn Logo and do some of the 
things I had hoped to see. I don't put that down; it was a signifi- 
cant finding. There was no doubt that some of the students did get 
an intellectual boost. Several who had been "average" students 
became straight A students, I felt confirmed and was beginning to 
dream ambitiously of really making a difference in how children 

174 » The Children's Machine 

learn. Seventh-graders are scarcely children, however, and I felt 
that if contact with computers were destined to have an important 
effect it would be at a much younger age. Yet it was obvious to 
me from the texture of the work that extending it downward in 
age was not simply a matter of developing teaching techniques. 
The more I got a deep feel for what it was like to work in the 
language as it was and to work on the kinds of projects we had 
been using, the clearer it became that my psychologist friends had 
been right: If this is what programming means, it's not for pre- 
formal children. Nevertheless, I knew there had to be another way 
to approach the problem. It needed a radically different idea. 

The idea took a while to come and an even longer while for me 
to recognize what it was. At first I was blocked by looking too 
hard for something too new in a way that often happens. After- 
ward you realize that you had the solution to the problem all 
along, but you couldn't see it because you were straining your 
eyes and stressing your mind looking out there into the great blue 
yonder. In this case I found the solution when I stopped taking 
myself so seriously and looking so hard for something new. The 
new idea came from looking in a more relaxed way at what was 
in hand. 

I was doodling at the computer as I often do by writing little 
programs with no particular importance or difficulty in them- 
selves. You could call it just playing. I don't know what such 
activity does for the mind, but I assume it's the same as what 
happens when one draws patterns or pictures with pencil on 
paper while thinking or listening to a lecture. What happened this 
time came from thinking that writing programs can be like draw- 
ing in many ways. In a way the Twenty-one program is a represen- 
tation—might one say a kind of picture-— of the form of a mental 
process, just as a pencil and paper drawing can be a representa- 
tion of a physical shape. The knowledge engineer's manner of 
work even has something in common with the portraitist's. The 
artist looks at how a person appears and tries to capture features 
in the medium of pencil and paper or paint and canvas. The 
knowledge engineer looks at how a person acts and tries to 

Computerists • 175 

capture essential features in a computational medium. These 
analogies quickly become strained, but they led to a shift in my 
perception of what was important in the Twenty-one program. 
Previously I would have said that what was important about the 
program was that it represented a kind of thinking. Now I wanted 
to say that what counted was that it represented something the 
programmer does. It didn't matter that the something was think- 
ing; it could just as well have been walking or drawing or what- 
ever. In fact, maybe walking or drawing would be better than 
playing Twenty-one; children care more and know more about 
these activities. 

The turtle came from thinking about how on earth a child could 
capture in computational form something physical like drawing or 
walking. The answer was a yellow robot shaped rather like R2D2 
and, like him, mounted on wheels. Nowadays we have much 
smaller robots with computers inside them. We also have turtles 
that exist only on a computer screen. In those days the turtle was 
a large object, almost as big as the children who were using it, 
connected by wires and telephone links to a faraway computer 
that filled a room. One could order it around by giving instructions 
in proper Logo grammar. As for words, a few were built-in (in- 
nate), and one could communicate in Logo to the computer that 
one wanted to define a new word. What was most remarkable 
was that by giving Logo the handful of new commands needed to 



LEFT 15* 




LEFT 90 


A turtle path showing commands FORWARD, RIGHT, LEFT. 

176 • The Children's Machine 

control the turtle, the spirit of what could be done with it changed 
dramatically. Where the day before I was worrying about how to 
descend a year from the seventh grade, now there was an area of 
"baby AT that seemed plausibly accessible to children well below 
school age. 

We have met the essential commands. Typing FORWARD 50 
causes the turtle to move in the direction it is facing a certain 
distance, which is to be called fifty turtle steps. Typing RIGHT 90 
makes it do what in the military would be ordered by Ri-i-i-i-ght 
TURN! The turtle stays where it is and turns in place. If it is already 
moving when it gets the instruction (though this was not possible 
in older forms of Logo that permitted just one instruction at a 
time), it changes direction and continues moving in what has now 
become the direction it is facing. 

But why should a child want to do this? And why should we be 
happy if a child does it? 

When I saw children playing with the turtle they told me a 
simple elemental answer that resonated with the preoccupations 
I have mentioned in the last few pages. Their first step toward 
expressing their answer was jumping all over the turtle and de- 
manding rides. Step 1: They clearly liked it. When the adults held 
back they asked one another to type commands to make the turtle 
move. Step 2: They took charge and used it for their own pur- 
poses. Some time later children began exercising ingenuity in 
giving commands that would produce interesting paths FOR- 
WARD 50 BACK 40 RIGHT 10 (and keep repeating that) does 

Combining the command REPFAT with the others. 

Computerists • 177 

something that some people enjoy. Step 3: It leads to invention. 
Step 4: It leads to the mathematical discovery that the commands 
FORWARD and RIGHT are a universal set in the sense that they 
can be combined to produce any possible path or shape. 

Intellectual problems about conceptualizing thinking and the 
role of computers that had been troubling me began to seem 
tractable. I watched a boy trying to get the turtle to write his name. 
He wanted an A. This required developing a little theory of the 
geometry of an A. It is not obvious how much the turtle should 
turn nor how much it should advance. This is real geometry. But 
it differed from School geometry in a cluster of important respects. 
First, it was a real problem that had come spontaneously to this 
boy. Of course, that can happen in regular geometry too. But it is 
very much more likely to happen here. Second, one visibly works 
toward the goal by being wrong most of the time. But one can see 
that one is wrong and ask oneself or someone else what hap- 
pened. The movements of the turtle externalize one's conception 
so one can think and talk about it. One can also do some of the 
kinds of "problem solving" that people do in the real world, such 
as solve another problem instead, or borrow a solution from 
someone else and adapt it to fit your case. 

The boy trying to make an A did just that. Initially he wanted 
to make a 45-degree angle at the top, so he instructed the turtle 
FORWARD 50 RIGHT 45 FORWARD 50. This led to a shock, as 
you see by following the picture. What happened? He looked at 
the wrong angle — the angle the turtle turns is what they call the 
"external angle" in geometry. This kid didn't know that, but he got 
the idea. So after some trial and error and computing he typed 

S~ A y\ 


Fumbling toward an A, following a model of the A as two leaning 
lines with a crossbar. Successive attempts are closer. 

178 • The Children's Machine 

fd 20 

-peat 3 tM 50 rt 120] r-ep Mt 3 [fd 50 rt ,20] 

T , J ri 6 ° ^ 50 rt 60 fd 20 

The new model: The A is a triangle with two less The m f 

the proced is: Draw j leg (fd * then 

manuever the turtle to be in place for the otheTleT To S T 
steps, pay attention to the fact that repeat 3 (S 5 fJ^C n h J ^ 
the turtle back to the beginning. Wh7l20 ? £££ 
moves 360 in 3 pieces. 

was to ^ ^ cro5J pfece ^ first p _m 

Mary there could make a triangle I can ,1 nZ T ^ ° P? " 

add on extra legs and it will be an A He still had ,h 1. ! 
-king the fngle>but ^ 

tha helped him find out himself. In the end, th<Tw^ e 1 
luW not sZ^ YJ ^ t0 the idea that —P"^ 

w^ s of 2 2T ve 01 ,eaming but mppon d ^ rent 

my fire ii , r n,ng ' BUt 35 1 h3d watched children 
my first mklings of this marked the fact that I was seeing the 


TELEVISION pictures of the war over Iraq gave millions of 
people their most vivid view of cybernetic technology, in 
the form of the "smart" missile, which seemed to hover like 
an insect before lunging into the entrance of a hangar or other 

It is depressing to feel again that the best way to open a discus- 
sion is with a military image, but it reflects a real fact of life that 
has played a big role in the strategies that have guided my work. 
The people who forge new technological ideas do not make them 
for children. They often make them for war, keep them in secret 
places, and show them in distant views. Even when there is no 
deliberate concealment, there is a trend nowadays toward opaque 
packaging of instructive technologies. In a distant past everything 
a society knew might have been open to its children for use or 
playful imitation. Even in my youth technological objects were far 
more "transparent" than now. I know that it was important to my 
own development that I could see and at least think I understood 
the inner workings of trucks and cars, and eventually go through 
the rite of passage of tuning or even "decoking" an engine and 
reseating its valves. I believe that the fact that so many people 

180 • The Children's Machine 

grew up on farms where old tractors were kept going by ingenuity 
and wire and tinkering contributed to the famous American can- 
do mentality, and I wonder whether the opacity of modern ma- 
chines is another environmental danger — a danger to the learning 

The physicist Richard Feynmann has written eloquently about 
the role in his childhood of the transparency of old-fashioned 
radios, and when Sherry Turkle interviewed MIT computer sci- 
entists she found that he is far from alone in having his develop- 
ing mind shaped by the drama of those glowing personlike elec- 
tronic tubes. Can the microchip take their place? And it is not 
only technical objects that have become opaque. The Bronx Bo- 
tanical Garden conducted a survey that showed that many chil- 
dren know no prior origin for carrots than a can. I have myself 
known children who had not yet connected the chicken they eat 
with the chicken in the cute pictures in books. At their age I was 
used to seeing birds killed and plucked and singed, and would 
assert my right to remove the heart and gizzards for my first 
dissections there and then in the kitchen. The kitchen lore that I 
took in was surely richer because nothing came in cans or pack- 
ages or mixes. 

I do not suppose that all children were ever given full access to 
the ideas of any society. But at least in times of slower change, an 
equilibrium could be maintained between what society needed its 
members to know and the learning opportunities it offered (delib- 
erately or mostly not) to its children. Since there is no reason to 
suppose that this is true today, and since, in any case, it is no 
longer acceptable that blind social forces be allowed to assign 
stations in life through differences in access to learning, deliberate 
effort is needed to bring to children knowledge that was not 
intended for them. School, even at its best, is too sluggish and | 
timid to do this. In this spirit, Logo was fueled from the beginning ] 
by a Robin Hood vision of stealing programming from the techno- = 
logically privileged (what I would in those early days in the 1960s 
have called the military-industrial complex) and giving it to chil- 

Cybemetics • 181 

dren. The centerpiece of this chapter is another raid on the tech- 
nologists' treasure troves. 

Most people watching the missiles on TV would not have been 
able to give a better explanation, if asked how they worked, than 
that "they are programmed to do it." The booty I am after is a set 
of ideas (and technologies to allow children to appropriate them) 
that would allow a more specific answer. Of course the missiles 
are programmed. But they are programmed in a particular way, 
using specific ideas whose development has played an important 
role in the intellectual history of our century and whose implica- 
tions might play an even bigger role in the coming one. My hope 
is that for anyone who has appropriated these ideas, the smart 
missiles will become transparent and, with them, a whole range of 
technologies and areas of science. In fact, these ideas are so 
closely interconnected in so many domains of knowledge that I 
shall use them here as the basis for the exercise of designing a new 
"subject," which I see as a more valuable intellectual area for 
young people than those that have been sanctified by School. 

The outline of this new subject will emerge gradually, and the 
problem of situating it in the context of School and the larger 
learning environment will best be broached when we have it in 
front of us. Here I give a preliminary definition of the subject — 
but only as a seed for discussion— as that kernel of knowledge 
needed for a child to invent (and, of course, build) entities with the 
evocatively lifelike quality of smart missiles. If this kernel were 
going to be the whole subject, a suitable name would be "control 
engineering" or even "robotics." But the kernel is intended only 
as a staging area for making connections with other intellectual 
areas, including (among others) biology, psychology, economics, 
history, and philosophy. To take account of these interconnec- 
tions, the subject needs a wider and less technical name. I have 
adopted the word that mathematician Norbert Wiener chose for 
the title of his highly influential book Cybernetics.- Control and 
Communication in the Animal and the Machine. It is true that the 
word cybernetics failed to take firm root in English-speaking 

182 • The Children's Machine 

countries, but it did much better in other languages and has a 
better chance here for a second shot in a new, learning-oriented 
connotation. In any case it will do well as a provisional name for 
discussion in this book. 

The project of developing a subject one might call "cybernetics 
for children" includes but goes far beyond my earlier vision of 
developing a framework in which children could engage in ele- 
mentary artificial intelligence. The new plan shares with the older 
one the use of technology as a medium for representing behaviors 
that one can observe in oneself and other people. But the way it 
does this is different in three respects: The range of behaviors that 
can be represented will be much larger; the student's affective 
relationship to such work will be more intimate; and the underly- 
ing epistemology will be softer and more pluralistic. 

The smart missile shows one aspect of the larger range of 
behaviors represented, even though it has the intelligence of a 
wasp rather than of a chess player. The shift from AI to cybernetics 
widens the focus from prototypes of behavior with a primarily 
logical flavor (such as playing chess or matchstick games) to 
include prototypes with a more biological flavor. The prototypes 
go beyond the human to include animals and robots, and beyond 
fact to include fantasy. Even very limited experiments (some of 
which have been carried out in collaboration with the makers of 
Lego) on making cybernetic construction sets for children have 
already allowed nine-, ten-, and eleven-year-olds to build wonder- 
ful devices that they describe as "dragons," "snakes," or "robots." 
Thus the children's work belongs more to what has recently been 
called "artificial life" than to artificial intelligence, even though 
many of the best projects invented by children using the construc- 
tion sets are biological only in demonstrating function, rather than 
representing living creatures. For example, I have seen several 
versions of what the children called "living houses." In one such 
model house interior, lights go on and doors close when the 
outside lighting is dimmed; in another, windows and shutters 
close to conserve energy when the temperature falls; in yet an- 

Cybernetics • 183 

other, the house contains "active furniture" such as a wake-up 
bed — a buzzer representing an alarm clock sounds at a set time, 
and ten seconds later the bed tilts over if the occupant is still in it. 

The opportunity for fantasy opens the door to a feeling of 
intimacy with the work and provides a peep at how the emotional 
side of children's relationship with science and technology could 
be very different from what is traditional in School. Fantasy has 
always been encouraged in good creative writing and art classes. 
Excluding it from science is a foolish neglect of an opportunity to 
develop bonding between children and science. I felt that I was in 
the presence of something much more promising when I saw 
children using science and technology to try to make a dragon — 
their own dragon, which mobilized a very special kind of engage- 
ment because it came from their own fancy. By serving their 
intimate purposes, science and technology became much more 
deeply their own. In this respect the AI project was good for some 
children whose fantasies could be expressed by its particular kind 
of program, but was restrictive for those with a different kind of 
imagination. Like writing, and painting, and expressive multi- 
media, cybernetics as a creative medium has a better chance of 
being open enough to offer something to everyone — and to the 
extent that it does not, it offers better opportunities for us to work 
harder at extending its scope. 

Turning science into "used knowledge" has epistemological 
implications, because it allows richer ways to think about knowl- 
edge than a true/false epistemology based on authority. Knowl- 
edge comes to be valued for being useful, for being of a kind that 
can be shared with others, and for matching one's personal style. 
In a traditional class only the most articulate and boldest students 
can effectively argue when a teacher rules that some way of think- 
ing is not the right way. In an applied setting there is a better final 
court of appeal: "Look, it worked!" Cybernetics as a subject would 
share the general epistemological fallout that comes from the fact 
that it is used rather than simply learned, but has some specific 
epistemological contributions of its own. 

184 • The Children's Machine 

One such contribution can be seen by looking more closely at 
the smart missile though the prism of Suppes's remark to me about 
being precisely wrong and vaguely right. It may seem paradoxical 
to find support in the development of weaponry for a softer and 
more negotiational style of epistemology against the canonical 
hierarchical style. After all, one thinks of the military as hierarchy 
par excellence and of weaponry as everything that is most macho 
and least negotiational. Fortunately, one of the features of the 
softer epistemologies is a greater tolerance for what a harder- 
edged epistemology would count as inconsistency and paradox. 

When David used his sling to hurl a rock at Goliath's head, he 
was operating in the domain of the precisely right: The shot would 
have been worthless unless its aim was exact. The development of 
artillery gave value to being precisely wrong as well, for an artil- 
leryman who knew by how much a shot overshot or fell short of 
the target could correct his aim to bring the next one closer. Errors 
became a source of information. However, the artilleryman would 
still be working in the domain of precise calculation. Indeed, one 
of the factors that drove the development of computers was the 
increasing complexity of the calculations needed for such work, as 
the range of artillery increased. With the target out of sight and the 
projectile traversing a whole range of temperatures and atmo- 
sphere conditions en route, calculation and information were 
needed — and more and more of these until the limits of the 
unaided human brain were exceeded. Already in the nineteenth 
century the production of mathematical tables in which the artil- 
leryman could look up the settings for his shot had become a 
significant activity. By World War II the need had become so 
overwhelming that many top mathematicians were mobilized to 
the task, among them John von Neumann and Norbert Wiener, 
who became, as a direct result, leading pioneers in the emergence 
of computers and of computational thinking. 

The development of machines to calculate better tables fol- 
lowed a pattern discernible in the adoption of all new technolo- 
gies (including, as was noted earlier, in education): The first use 

Cybernetics • 185 

of a technology always consists of striving to do better what had 
been done before. In this case it was still a matter of "ready, aim, 
fire." Once the shell was on its way, it would land where the laws 
of physics and the accidents of the environment would place it; no 
deus ex machina would make a correction. Time and the growth 
of ideas are usually needed before the idea of using a new tech- 
nology to do something that had never been done before can 
even be conceived. In this case, the idea was that of making a 
weapon that would be brought by aim only vaguely to the right 
place and then turned loose to find its target. Only at this point 
(which was not actually reached during World War ID could one 
say that the technology was no longer being used to make quanti- 
tative improvements on traditional practice. Although the ultimate 
goal was the same, the means were more than just quantitatively 
different; they were epistemologically different in that they used a 
different way of thinking. 

Traditional epistemology is an epistemology of precision: 
Knowledge is valued for being precise and considered inferior if 
it lacks precision. Cybernetics creates an epistemology of 
"managed vagueness." This does not mean that it has loose stan- 
dards: The smart missile is expected to perform in the end even 
better than the traditional weapon. Cybernetics is based on a 
serious study of ways to make the best use of limited knowledge. 

With this last statement we get a glimpse of a specific cybernetic 
slant in epistemology. We are still far from capturing all it has to 
offer, but what we are concerned with here is cybernetics as a key 
to learning for children. We now turn, therefore, to some exam- 
ples of turtle programming that give a sense of how children can 
emulate the smart missile and learn by so doing about the man- 
agement of uncertainty. 

The turtle, it will be remembered, grew out of a concept of using 
programming as a medium for representing (or "sketching") one's 
own behavior. The geometric programs mentioned in the previ- 
ous chapter did this for behaviors assumed to be predetermined 

186 • The Children's Machine 

without any allowance for contingencies: For example, to draw 
the triangle, go forward 100 units, turn right 120 degrees, and 
repeat this twice. To underline the difference between that mode 
of describing a behavior and the cybernetic mode, I cannot do 
better than referring to a personal learning experience that was 
fresh in my mind when I first thought about turtles. As a student 
pilot I learned to make a sharp distinction between two modes of 
flying from point A to point B. One is called dead reckoning. 
Everything is plotted before you start. You measure the distance 
and the direction from A to B, you study the winds, and you make 
allowance for how they would blow you off course if you ignored 
them. Once in the plane, in principle you don't even need to have 
a map. Set your heading at 100 degrees, fly for 75 minutes at 150 
knots, and you will be there. The other method is called pilotage. 
In principle, you don't need to do any calculations on the ground; 
instead, you draw a line on the map from A to B, and as you fly 
you check landmarks on the ground against symbols on the 
map: Pass the tip of the lake ... TV tower about a mile on the 

Turtles, as they were described earlier, were programmed in the 
spirit of dead reckoning. Pilotage, however, needs something else: 
eyes to see. This form of navigation became possible for turtles 
when they were fitted with sensors and so could report to the 
computer on interactions with their environment. Many kinds of 
sensors have been used in this way: A touch sensor reports to the 
computer that it is being touched, a light sensor reports the inten- 
sity of the light falling on it, and sound sensors, temperature 
sensors, and others act in similar fashion. The turtle still follows a 
program, but the existence of sensors permits a different relation- 
ship between the turtle's program and its movements. The pro- 
gram of a "geometry turtle" specified the actual movement in a 
geometric sense: Go forward so much, turn right so much, and so 
on. The program of a "cybernetics turtle" might say, in effect, 
"Find a light and go to it." Of course, actually "saying" this re- 
quires more than having a sensor; it requires ideas about how to 

Cybernetics • 187 

use sensors to give a machine the ability to follow a goal. The 
program no longer follows a "blueprint," but now "emerges." As 
soon as children begin to use this emergent programming, they 
have stepped into the world of cybernetics. 

The newness of the world of cybernetics becomes apparent 
from resistances seen in children's switch from the predetermined 
programming of the geometry turtle to the interactive program- 
ming of the cybernetic turtle. For example, consider how to pro- 
gram a turtle with touch sensors to circumnavigate a square box. 
Many beginners will try to use dead reckoning: Measure the box, 
decide that its length is 130 turtle units, and try the program 
REPEAT 4 [FORWARD 130 RIGHT 90]. The logic behind this is 
clear: We are told that computers do exactly what they are pro- 
grammed to do, neither more nor less, and so the naive program- 
mer tells it to make exactly the movements needed to get around 
the box. 

Excellent insights into what cybernetic thinking is about come 
from contemplating various flaws in this logic. First note that this 
is a case where being too precisely right opens one to the risk of 
being disastrously wrong. The program will work if, but only if, 
everything goes exactly according to plan. It has ho margin for 
error. It will fail if the turtle turns a tad too soon or a tad too 
much. In practice, it would be almost sure to fail because not 
even computers — and certainly not physical objects like tur- 
tles — actually do exactly what they are expected to do. Error is a 
universal feature of the world, and in this case small errors can 
be disastrous. 

Another flaw in the exact-programming approach can be ap- 
preciated only by comparison with an alternative approach, a little 
more like pilotage and much more in the spirit of cybernetics: that 
of putting oneself in the place of the turtle. One wouldn't walk 
around the box by taking a precise number of steps, but rather by 
using pilotage — or what cyberneticians would call feedback. Just 
so as to walk to the corner and then turn, one would at every step 
adjust one's course so as to keep the box a few inches to the left. 

188 • The Children's Machine 

If one felt oneself too close, one would turn away slightly to the 
right; if one were too far, one would turn slighdy to the left. This 
can easily be translated into a program that repeats over and over 
the following cycle of instructions: 

TEST LEFT-TOUCH < — This causes the touch sensor to 

report either 

IFYES [RIGHT 2] <— bumping the box, so turn away 

a little, or 

IFNO [LEFT 2] •<— losing the box, so turn toward t 

it a little, then 
FORWARD 2 <— take a step 

The reader may ask why the number 2 was chosen. The won- 
derful answer is that the program would work with 5 or 1 or 0.5 
in place of 2. As long as the turtle turns ("vaguely") a little left or 
a little right and moves a little forward, it will get around the box. 

The most remarkable feature of this program is its vagueness as 
to the size and shape of the box. The size of the box does not 
show in the program, and this is a strength because it means that 
the program will work for a box of any size. Even more remark- 
ably, the size of the angle to be turned at each corner does not 
show either, which means the program will work for an object of 
any shape as well as any size! 

Nobody who has seen both approaches (let's call them for the 
moment the geometric and the cybernetic) ever has any doubts 
about which is better for this job. The geometric approach is 
precarious and particular. Even if it does work for the box, it will 
fail if tried on, say, a circular object. The cybernetic approach is 
robust and very general: It will work every time on almost any 
object to be circumnavigated. Yet in my experience, many if not 
most people who meet the problem cold will prefer the geometric 

Why is this? One factor, of course, is lack of experience with 
cybernetic situations. But I think that a more powerful factor is a 

Cybernetics • 189 

supervaluation of the "abstract" and "mathematical" acquired 
from the general culture and especially from School. By the same 
token the success of the cybernetic approach contributes to the 
revaluation of the concrete. In this case, concrete surely means 
putting yourself in the place of the turtle as you imagine it going 
around; and doing so with an open mind should raise doubts 
about the geometric approach as well as heuristically suggesting 

the cybernetic one. 

The "vague" cybernetic approach is, moreover, universal— 
that is it will work with any kind of sensor. For example, think 
of a turtle with a light sensor on each side. The problem is to 
program the turtle so that if a light is placed in its field, it will 

go to it. . . 

A classical programming approach would suggest an exact imi- 
tation of the dead-reckoning procedure for airplanes: Split the 
problem into two parts, first determine where the light is, and then 
go there. Putting this plan into practice needs some mathematical 
technique which I will omit since what is most interesting here is 
the extraordinary simplicity of the cybernetic method. The key 
fragment of a workable program is: 

TEST LEFT-SENSOR-*- RIGHT-SENSOR-*- Is light stronger 

on left? 

IFYES [LEFT 10] ««— Turns turtle toward the light 
IFNO [RIGHT 10] -«- Ditto 

FORWARD 5 • «*- In any case, move forward a little 

What is interesting here is again the extreme vagueness of the 
turtle's knowledge about where the light is located. If the light is 
anywhere to the left, the turtle turns left; if it is anywhere to the 
right it turns right. If the light is too near the center, the turtle 
makes what is effectively a random turn one way or the other. Yet 
this will eventually bring the turtle to the light— not approxi- 
mately to the light, but right there! 

190 • The Children's Machine 

A saying tells us that the chain is no stronger than its weakest link. 
In this it is not expressing a universal truth but the ideology of 
linear hierarchical thinking. Many classical computer programs, 
many mechanisms, and many logical arguments are constructed 
in such a way that the whole will work only if every part is exacdy 
right. A fundamental tenet of cybernetics is that living systems do 
not work like that; and, moreover, the principles by which they 
escape the apparently inexorable truth of the saying are of great 
importance not only for understanding biology but for designing 
technologies and for conducting social and personal life. Much of 
the attraction of early cybernetics came from the apparent magic 
of systems that worked much better than their pans. Claude Shan- 
non, the founder of modem information theory, had constructed 
amazingly efficient error-correcting codes: Even if a noisy cable 
caused an extra blip here and there, a decoding device at the 
receiving end could reconstruct the message. Frank Rosenblatt 
had built a kind of computer called a perceptron which had the 
wonderful ability of continuing to work with only gradual deterio- 
ration of performance as one plucked out its parts at random. 
(Don't try that on your PC.) Warren McCulloch, the polymath who 
should be counted with Wiener as co-founder of cybernetics, 
wrote eloquently about how our brains keep functioning recog- 
nizably even though tens of thousands of neurons die every day, 
and how pouring such chemicals as alcohol into the system 
changes the behavior of the individual cells far more than the 
behavior of the whole. And, of course, if our light-seeking turtle 
makes a mistake every now and then it will follow a different path 
but still get to the goal — in fact, it will eventually get there even 
if its decision about which side gets more light is randomly wrong 
most of the time. 

The purpose of noting that a system can be more reliable than 
its components is not a blanket exoneration of mindless sloppi- 
jiess. If one wired the turtle so that right and left were inter- 
changed, the program we wrote would never bring it to the 
light — quite the contrary, it would be photophobic and flee light. 

Cybernetics • 191 

On the other hand, a fifth-grader with a little cybernetic experi- 
ence could write a different and not very much more complicated 
program that would adapt to such mistakes in wiring. Cybernetics, 
in fact, is full of principles of adaptation to a world that can never 
be exactly predicted or completely controlled. These principles 
have names like "redundancy," "systemic thinking," "statistical 
trend," "self-organizing system," and "feedback." Most of what 
follows applies to the other principles as well. Here, however, I 
focus on feedback, taken as an example both to show what kind 
of idea cybernetics breeds and, in particular, to justify the choice 
of cybernetics as knowledge to be made available to children. 

Two extreme answers to the question of choosing such knowl- 
edge must be rejected. The extreme position on the conservative 
side is to follow what is already in the school curriculum: There 
is already more there than children seem to be able to learn; 
reformers will do better to improve teaching what is there than 
aggravating the situation by quixotically proposing new subjects. 
But on my reckoning, the fraction of human knowledge that is in 
the curriculum is well under a millionth and diminishing fast. I 
simply cannot escape from the question: Why that millionth in 
particular? In any case, plenty of people are busy polishing the 
established millionth (or billionth or whatever it actually is), so the 
few of us who seem willing to explore elsewhere will not be 

The radical answer is that we should make all knowledge avail- 
able so as not to impose our own prejudiced views on the next 
generation. In my discussion of Jennifer and the Knowledge Ma- 
chine I myself proposed something like that in a long-term ap- 
proach to factual knowledge. Yes, I do think that children should 
and one day will have free access to knowledge about Africa and 
Tibet as well as America and Europe, about giraffes and elephants 
as well as cats and dogs, about Shaka and Dingaan and their 
descendants as well as King George and his descendants. 

If I could make such a Knowledge Machine, I would. But no 
one person can. The only way to approach its ever coming into 

192 • The Children's Machine 

being is through systemic thinking. The crucial question for me is: 
What can I do now to speed the necessarily social process that can 
lead to the eventual development of the Knowledge Machine or, 
rather, of the better idea that is sure to take us all by surprise when 
it emerges? My answer is to follow my intellectual sensors and try 
as I go to articulate the criteria that draw me to cybernetics as a 
choice for the billionth of human knowledge that is as much as 
one person can try to make directly available. 

One criterion shouts for attention: Is there a billionth that will 
be especially effective in opening doors to much larger areas and 
giving 'people more freedom to make personal choices? To see 
whether a concept is capable of playing this role, we must see 
whether it possesses the qualities of appropriability and generativ- 
ity. The meaning of these concepts will emerge from a discussion 
of why feedback qualifies as a mathetically powerful idea by its 
strength on both counts. 

Evidence for the appropriability of the concept is that this has 
already happened on a large scale. Books on wildflowers use a 
vocabulary of "escaping from cultivation" and becoming "natural- 
ized." It is not hard to trace a route by which the word feedback 
escaped from cultivation in the esoteric language of such people 
as radio engineers, who used it to describe a technique for stabiliz- 
ing an amplifier by "feeding" a fraction of the output "back" to the 
input. By the 1940s the concept of feedback had developed into 
a form that will be the theme of this chapter and was gaining 
recognition as important in many branches of engineering and 
also in physiology. 

The excitement around this early form of cybernetics (which 
would not be called that until 1948) drew in a number of people 
whose interests were in neither engineering nor physiology. Typi- 
cal and most influential of these was anthropologist Gregory Bate- 
son, who saw that these ideas could be important in understand- 
ing human behavior. Bateson became a central figure on the 
psychological scene in the 1960s; and through this channel, ideas, 
and certainly words, from cybernetics spread into popular cul- 

Cybernetics • 193 

tures that were even further removed from anything technical, 
indeed, that were profoundly antitechnical. Thus the stage was set 
for a general amnesia about the technological origin of the word 
that became very clear to me when I conducted an informal poll, 
asking acquaintances what the word feedback suggested to them. 

Most spoke about responsiveness in human relationships. A 
teacher spoke about the need to "get feedback" from her class. A 
friend who had experience with family therapy spoke about how 
spirals of a worsening relationship come about when a person's 
anger gives rise to behaviors in other people that aggravate that 
person's anger. This use of the word is closer to the technical 
origin than the teacher's, but my friend was not aware of any such 
connection and was quite surprised by the fact that the spiral 
buildup of anger could be modeled physically by placing the 
microphone of a public address system near the loudspeaker and 
turning up the volume control: A little sound whispered into the 
microphone produces a sound from the loudspeaker that "feeds 
back" into the microphone. If what feeds back is even ever so 
slightly louder than the original whisper, a self-perpetuating and 
self-augmenting process is created, and very soon the room is 
filled with an ear-splitting whine. The phenomenon is called "pos- 
itive feedback." Whenever a state of a system, say, the anger level 
or the sound level, produces effects that augment that state, there 
is positive feedback; and when there is positive feedback, the 
anger or the sound or whatever it is will grow until something 
snaps or blocks. 

Another sign of the concept's appropriability is the ease with 
which it is taken up in humor. One of my students reported an 
example of a real event that shows this feature. A couple, let's say 
A and B, share a bed with an electric blanket. In this case the 
blanket provided separate dials for the two sleepers, so that the 
heat could be separately adjusted on each side of the bed. At least, 
that was what was intended. On one occasion the dials got 
crossed, so that A, on the left side, held the dial that controlled the 
heater on the right side, and vice versa. A woke up feeling cold, 

194 • The Children's Machine 

and turned up the dial expecting to get more heat. But the extra 
heat was generated on B's side, and B, feeling hotter, turned the 
heat down. A became even colder and turned the heat even 
farther up. So B got even hotter and turned the heat even farther 
down. Now A was really shivering and turned the heat to maxi- 
mum. The effect is to raise B's side to roasting temperature and 
reduce A's temperature even more. If they didn't know it before 
A and B certainly knew something about positive feedback after 
they sorted this one out. 

Negative feedback, which is more useful and more intriguing 
does the opposite. The simplest model is a thermostat that con- 
trols heat and air-conditioning. Set the dial to 70. If the room *ets 
hot, that is to say, above 70, the thermostat starts the air-condition- 
ing The feedback is called negative, because the state of heat 
produces an effect that will reduce heat, and the state of cold 
produces an effect that will reduce cold. In one sense no mecha- 
nism could be more simple. Yet many have been impressed by the 
quality this system shares with living beings: It acts as if it had a 
purpose as if it is determined to keep the temperature at the set 
level of 70 degrees. 

Some people have engaged in philosophical discussion about 
whether a thermostat really has purposes or goals. To me this 
smacks of rather futile wordplay if it is pursued in a spirit of 
seeking the ultimate truth one way or the other, though there are 
ways to pursue it that could make for valuable discussion among 
children of epistemological and psychological principles. But the 
pragmatic discovery that the principle can be used to design ma- 
chmes that behave as if they are following goals is basic to modern 
technology. The fact that the thermostat seems to have the goal of 
keeping the temperature in the house constant does not stir me 
particularly. But however much I know about how such things 
work, I still find it evocative to see a Lego vehicle follow a flash- 
light or turn toward me when I clap my hands. Is my reaction a 
streak of residual metaphysics? Is it because the little thing seems 
somehow betwixt and between? I know that it isn't alive but it 

Cybernetics • 195 

shares just enough with living beings to excite me — and many 
others too. Whatever the reason, such things are intriguing and 
making them is an exciting way to engage with an important body 
of knowledge. 

What makes the principle even more remarkable is that it is also 
generative: It can be used to understand many situations, and 
some in very surprising ways. It is rich in intellectual jokes and 
comic or paradoxical situations. 

We already had one comic situation with the double electric 
blanket. In the same spirit, here is a tricky question: How can you 
use a piece of ice to heat a room? A better quiz question than yet 
another repetition of calculating the volume of a gas if it is heated 
20 degrees. Well, the answer is: You put it on the thermostat! What 
does that do? It makes the thermostat think the room is cold, so 
it turns on the heat. As long as the ice is there, the heat will go full 
blast. The room will become as hot as the heating system can 
make it. 

Our body temperature is maintained by a thermostat that is 
more complex than the simple one that keeps the room comfort- 
able. But its principle has to be the same: Somehow the system 
must know whether the temperature is above or below the set 
level — in this case, about 97 degrees Fahrenheit. If the tempera- 
ture is less than the set level, a process is put into motion that will 
raise the temperature— for example, shivering and constricting 
the blood vessels near the skin. The movement of the muscles 
generates heat, and the vasoconstriction reduces its loss. If the 
temperature is above the set value, a process is put into motion 
that will decrease it — for example, panting, sweating, and dilation 
of superficial blood vessels. 

That much is easy to understand. But here's a trick question. 
When you have a fever you are hot, and you also often shiver. Yet 
shivering is a reaction to cold. How come you are hot and shiver? 

The question is a nice example of an engaging paradox. The 
answer comes from noticing that being hot and being cold are 
relative. When you have a fever you are hot compared with the 

196 • The Children's Machine 

normal temperature. But you may not be hot compared with the 
set level: A fever makes you hot by the equivalent of raising the 
thermostat setting so that the normal mechanisms for adjusting 
body heat operate to keep you at the new set temperature. 

Another phenomenon that is explained by the body setting a 
"goal level" for a feedback mechanism is one that frustrates dieters 
in their attempt to lose weight. It appears that the body "tries" to 
maintain a certain weight level by adjusting the rate at which 
energy is dissipated. If this weight level is not the one that the 
person desires, a conflict of wills is created between the person's 
goals and that of the feedback mechanism governing weight: 
When body weight falls below the level set for the feedback 
system, the mechanism sets processes in motion to increase 
weight or at least slow the fall. 

Since it is not possible to discuss everything at once I glossed over 
a difficulty we had encountered when we first tried to work with 
the touch-sensor turtle. Pilot experiments about twenty years ago 
showed that these ideas were accessible to children. Fifth-graders 
could carry out assignments requiring the use of feedback, but for 
most children these stayed on the level of assignments, in marked 
contrast to the way in which their graphics activities took on a life 
of their own. 

My first shot at fixing the problem is worth mentioning here 
even though it led up a blind alley, since it illustrates an educa- 
tional developer's knee-jerk response to a difficulty. In addition, it 
shows how hard it was for me to grasp the significance of what 
was already being learned from the experience with graphics. Our 
problem seemed to be much like the one we faced in the first Logo 
classes. This observation led to a blind alley in the following way. 
At that time, we had solved the problem by creating the turtle, so 
we should solve this one by making more creatures. This would 
give children more choice and so generate more enthusiasm. The 
upshot was that we made a range of new computer-controlled 
objects, of which the most memorable were a pneumatic worm 

Cybernetics • 197 

and a wooden puppet. We and some of the children had fun, but 
all this was beside the point. 

The real problem was that I was still thinking in terms of how 
to "get the children to do something." This is the educator's 
instinctive way of thinking: How can you get children to like math, 
to write wonderfully, to enjoy programming, to use higher-order 
thinking skills? It took a long time for me to understand in my gut, 
even after I was going around saying it, that Logo graphics was 
successful because of the power it gave to children, not because 
of the performance it got from them. Drawing was something 
already rooted in their culture; with the computer they took some- 
thing that was already theirs into new (don't say "better") direc- 
tions. For that matter, dealing with images on screens was already 
in their lives and important to them; the graphics turtle offered 
them new ways to relate to these images. Representing behaviors 
by programming a cybernetics turtle did not have roots in the lives 
of most children. 

Nevertheless I had a hunch that cybernetics was a world chil- 
dren would like and profit from. I continued fretting over the 
problem. Though the solution was simple enough in concept 
when it came, it came slowly and took many years to implement. 
The point was to give up trying to entice children into my cyber- 
netic world of turtles and instead to put cybernetics into their 
world. This idea, which took shape in the mid-1980s, is what led 
to my collaboration with Lego. Children love constructing things, 
so let's choose a construction set and add to it whatever is needed 
for them to make cybernetic models. They should be able to make 
a turtle with motors and sensors, and have a way to write Logo 
programs to guide it; or if they wished to make a dragon or a truck 
or a wake-up bed, they should have that option too. They should 
be limited only by their imaginations and technical skills. In early 
experiments with this concept, the motors and sensors had to be 
connected to a computer via an interface box. More recently we 
have built computers small enough to go into the models them- 
selves. The difference feels substantial; now the intelligence really 

198 • The Children's Machine 

is in the model rather than in an ouf-of-scale computer. Besides, 
the models can now be autonomous. They can range far afield 
without an umbilical cord. It all makes it more real. 

However, the biggest shift in the development of the Lego-Logo 
toward being "real" in the lives of children will come when the 
activity moves out of school into the home. Looking toward the 
future, it seems obvious that children will grow up building cyber- 
netic constructs as fluently as they now build cars and houses or 
train-track circuits. Only then will cybernetic thinking really 
become part of their culture. 

This fact goes a long way toward answering the two questions 
about Lego-Logo most often asked by parents and teachers: What 
will they learn from it? And won't it favor boys over girls? In my 
own mind, the answers to both questions are rather different from 
what most questioners are driving at. The first question concerns 
what piece of the school curriculum is being learned, but I attach 
most importance to such issues as children's relationship with 
technology, their idea of learning, their sense of self. As for the 
gender issue, I am thinking more about how in the long run 
computational activities will affect gender than about how gender 
will affect the activities. For gender is not mainly a matter of 
biology, it is a social construct; and the degree of change I antici- 
pate in children's lives will surely one way or another result in a 
different construct. What I do think is important is for women to 
participate in forming the computer culture of the future. 

But having made these remarks in a spirit of provoking reflec- 
tion, I turn to the more immediate kind of question, giving an 
example of a very specific kind of learning through Lego-Logo. 
Sooner or later in building objects with Lego, students run into the 
need for gears. Their work provides good examples of material 
that overlaps with School science and math, and of an alternative 
style applied to these subjects — instead of a formal style that uses 
rules, a concrete style that uses objects. 

The motors in the construction set turn at a high speed with low 
torque. A car built by attaching these motors directly to the wheels 

Cybernetics • 199 

will go very fast, but will be so underpowered that the slightest 
slope or obstruction will cause it to stall. The solution to the 
problem with Lego cars is the same as that adopted by designers 
of real cars: Use gears. Yet in order to use them effectively, chil- 
dren need to understand something about gear ratios. This in 
turn brings with it a cluster of ideas such as force, torque (the 
physicist's measure of the "force" of turning), and mechanical 

An aspect of this knowledge, which is on the cutting edge of 
learning for children of elementary school ages, is its rational, or 
relative, aspect. If a small gear drives a larger gear, the larger gear 
will turn more slowly and with greater torque. It is the relative and 
not the absolute size of the two gears that counts. But many 
children at this age, mainly boys, tend to reason as if the size of 
only one gear matters — as if they were following a set of rules 
such as "large gears are slow and strong" and "small gears are fast 
and weak." (See illustration on page 200.) Without the notion of 
relative size, such rules fail. Other children, predominantly girls, 
are less articulate and more physical in their explanations. They 
squirm and twist their bodies as they try to explain how they 
figure things out, and they get the right answer. 

Theorists who look at intellectual development as the acquisi- 
tion of increasingly sophisticated rules would say that children run 
into problems if the rules they have built are not yet good enough. 
The idea of concrete thinking enables us to consider a different 
kind of theory. Our observations suggest that the children who 
did well did not have better rules, but a tendency to see things in 
terms of relationships rather than properties. They had access to 
a style of reasoning that allowed them to imagine themselves 
"inside the system." They used a relationship to the gears to help 
them think through a problem. 

This "reasoning from within" may not be adequate for all prob- 
lems with gears, but for the kind of problem encountered by the 
children in our project it was not only adequate but much less 
prone to the errors produced by a too simple set of rules. 

200 • The Children's Machine 

Relational, concrete thinking puts you at an advantage: You do 
not suffer disaster if the rule is not exactly right. This suggests 
though all this is still highly speculative, that there may here be 
pockets of physical scientific knowledge that are more accessible 

to girls than to boys. 

I defined bricolage as a style of organizing work that can be 
described as negotiation^ rather than planned in 
Warren McCulloch called "hierarchical" rather than h.erarch^aL 
The example of the children and their gears serves to introduce 

Cybernetics • 201 

another characteristic displayed by many bricoleur programmers, 
which Turkic and I have called "proximality," or closeness to the 
object. A programmer like Kevin is closer to his computational 
objects than someone like Jeff. Like the children who "reasoned 
from within" with the gears, Kevin psychologically places himself 
in the same space as the screen turtles. He experiences his space- 
ship as tangible, sensuous, and tactile. He is down there, in with 
the sprites, playing with them like objects in a collage. Kevin talks 
about these objects using gestures of hand and body that show 
him moving with and among them. In speaking of them, he uses 
language such as "I move here." 

I chose Kevin, a boy, to illustrate "reasoning from within" in 
order to avoid overstating the correlation with gender of behav- 
iors that are, however, more characteristic of girls. The general 
idea I want to stress is that the relationships among gender, tech- 
nology, and hard science take on new aspects in a context where 
children can work intimately with physical computational objects. 
This gives cybernetics another claim to be a new subject that will 
open new intellectual domains to children. 

I next turn to some more sophisticated concepts in the same 
general area as cybernetics. To begin with, consider an experi- 
ment reported by my colleague Mitchel Resnick using a version of 
Logo that he calls 'Logo (Star Logo), which, among other things, 
allows for very large numbers of turtles. In his Ph.D. thesis, Re- 
snick talks about a "centralized mindset," which leads people to 
postulate a directing agent, rather than look for explanations as 
emergent from decentralized interactions. 

Two high school students who had recently received their 
driver's licenses decided to use "Logo to show cars moving on a 
highway. The students started by creating several dozen turtles, 
each representing a car, and then wrote a very simple program for 
each car. The program consisted of two simple rules. If a car 
sensed another car ahead of it, it slowed down. If it didn't sense 
another car, it speeded up. With this simple program the students 
did not expect much to happen, but when they ran it, the cars 

202 • The Children's Machine 

bunched into a realistic-looking traffic jam. The students were 
surprised to see such a complex pattern forming from their simple 
little program. Indeed, the program provided a striking example of 
self-organization: The cars seemed to form themselves into a pat- 
tern without any centralized control. The jam just emerged from 
the interactions among the individual cars, but the students felt 
there must be a "cause." 

This same idea comes up in all areas of science. In biology, ants 
organize themselves into trails to look for food; birds organize 
themselves into flocks so as to migrate; on longer times scales, 
genes organize themselves into new creatures. It is worth noting 
that the students appreciated the self-organizing nature of the 
traffic jam only because they had written the programs themselves. , 
Had they been using a packaged simulation, they would have had 
no way of knowing the elegant simplicity of the programs under- 
lying the jam. 

When the students started watching the traffic jam, they were in 
for another surprise: The traffic jam moved backward. They found 
this behavior counterintuitive. How could a traffic jam move back- 
ward when all of the cars within it were moving forward? This 
behavior highlighted an important idea: Emergent structures often 
behave very differently than the elements that compose them. This 
idea is true not only for traffic jams but for a much wider range of 
phenomena, including waves. Ideas about waves are notoriously 
difficult for beginning students to grasp. One reason is that waves 
are often presented in unmotivated contexts (such as moving 
along a string) or as a difficult mathematical formalism (a differen- 
tial equation). The 'Logo traffic program provided a much more 
meaningful introduction to such problems, especially since the 
students had recendy received their driver's licenses. Moreover, 
the waves were generated by an accessible formal system, a set of 
simple computer programs. Furthermore, since the students wrote 
the programs themselves, they were able to manipulate the pro- 
grams to explore many different wavelike phenomena. 

The examples of the traffic jam and the gears show how cyber- 

Cybernetics • 203 

netic ideas connect with concepts in the physical as well as in the 
biological sciences on both the advanced and the elementary 
levels. In this way, cybernetics possesses a combination of appro- 
priability with richness of scientific connection. In addition to its 
connections with classical science, cybernetics is closely related to 
another modern area of knowledge often known as "systems 
theory," which in turn is closely connected with ways of thinking 
that are prominent in economics, ecology, and the study of evolu- 
tion. The same kind of thinking that went into programming and 
then understanding the traffic situation can be applied with the 
same ease to situations in which there are several kinds of objects, 
for example, two species of animals, one a predator and the other 
its prey, and a plant that is eaten by the second animal species. In 
a few hours' work a junior high school student can set up a 
microworld with populations of the two animals and the plant, by 
specifying how much each animal eats per unit time, and how 
frequently all three species breed and die. 

I conclude by saying something about the implications of this 
kind of work for the concept of programming. It is an adage 
(attributed to Lady Lovelace in the nineteenth century) that a 
computer does exacdy what it is told to do, neither more nor less. 
But a cjeep ambiguity inherent in this statement becomes apparent 
if one compares the two turtles moving around a square box, one 
following a geometric and the other a cybernetic program, that 
were mentioned earlier. Are they doing exactly what they were 
"told" to do? If "telling" means actually writing it explicidy in the 
program, then one could say that the geometric turtle was "told" 
to go around the box. What the cybernetic turtle was told, how- 
ever, looks very different; in fact, it might need some thinking to 
decide that its program would make it go around the box. There 
is a distance between what it was told and those aspects of its 
behavior that interest the programmer. In other cases the distance 
been program and result can be even greater. An example that is 
familiar to anyone who has done much Logo is the program that 
draws a circle by doing REPEAT 360 [FORWARD 1 RIGHT 1). Was 

204 • The Children's Machine 

the turtle told to draw a circle? If one says yes, one must say that 
it was told this in a very odd way. 

Earlier, I made a distinction between dead reckoning, or blue- 
print programming, and pilotage, or emergent programming. In 
the next chapter I shall use the language of blueprint and emer- 
gent programming to talk about economics and other "systemic" 
situations. I think it will appear that experience in the kinds of 
work discussed in this chapter will prepare young minds for the 
issues discussed there. 


What Can Be Done? 

WHEN one is overwhelmed, as everyone must be from 
time to time, by a sense that School is too firmly im- 
planted ever to change, it is helpful to contemplate the 
political changes across the globe that were until recently consid- 
ered quite impossible. The events in what we used to call the 
Soviet bloc are the most dramatic, but developments in South 
Africa, Chile, and Central America are in the same class. 

The sight of crowds demolishing the Berlin wall, or of Nelson 
Mandela sitting at a negotiating table with Frederik de Klerk, is a 
potent antidote to any tendency to say, "It can't happen." But the 
way these things did happen is sobering as well as heady. A closer 
look carries many lessons about the pain and difficulty of chang- 
ing a large, stable, well-rooted social structure. One of the most 
important of these is about how a system defends itself against 
recognizing the depth of its problems and the need for fundamen- 
tal change. 

Mikhail Gorbachev, whose name has deservedly become em- 
blematic of change, is also one of history's most interesting exam- 
ples of resistance to change. Even as he ushered in previously 

202 • The Children's Machine 

bunched into a realistic-looking traffic jam. The students were 
surprised to see such a complex pattern forming from their simple 
litde program. Indeed, the program provided a striking example of 
self-organization: The cars seemed to form themselves into a pat- 
tern without any centralized control. The jam just emerged from 
the interactions among the individual cars, but the students felt 
there must be a "cause." 

This same idea comes up in all areas of science. In biology, ants 
organize themselves into trails to look for food; birds organize 
themselves into flocks so as to migrate; on longer times scales, 
genes organize themselves into new creatures. It is worth noting 
that the students appreciated the self-organizing nature of the 
traffic jam only because they had written the programs themselves. , 
Had they been using a packaged simulation, they would have had 
no way of knowing the elegant simplicity of the programs under- 
lying the jam. 

When the students started watching the traffic jam, they were in 
for another surprise: The traffic jam moved backward. They found 
this behavior counterintuitive. How could a traffic jam move back- 
ward when all of the cars within it were moving forward? This 
behavior highlighted an important idea. Emergent structures often 
behave very differently than the elements that compose them. This 
idea is true not only for traffic jams but for a much wider range of 
phenomena, including waves. Ideas about waves are notoriously 
difficult for beginning students to grasp. One reason is that waves 
are often presented in unmotivated contexts (such as moving 
along a string) or as a difficult mathematical formalism (a differen- 
tial equation). The 'Logo traffic program provided a much more 
meaningful introduction to such problems, especially since the 
students had recendy received their driver's licenses. Moreover, 
the waves were generated by an accessible formal system, a set of 
simple computer programs. Furthermore, since the students wrote 
the programs themselves, they were able to manipulate the pro- 
grams to explore many different wavelike phenomena. 

The examples of the traffic jam and the gears show how cyber- 

Cybernetics • 203 

netic ideas connect with concepts in the physical as well as in the 
biological sciences on both the advanced and the elementary 
levels. In this way, cybernetics possesses a combination of appro- 
priability with richness of scientific connection. In addition to its 
connections with classical science, cybernetics is closely related to 
another modern area of knowledge often known as "systems 
theory," which in turn is closely connected with ways of thinking 
that are prominent in economics, ecology, and the study of evolu- 
tion. The same kind of thinking that went into programming and 
then understanding the traffic situation can be applied with the 
same ease to situations in which there are several kinds of objects, 
for example, two species of animals, one a predator and the other 
its prey, and a plant that is eaten by the second animal species. In 
a few hours' work a junior high school student can set up a 
microworld with populations of the two animals and the plant, by 
specifying how much each animal eats per unit time, and how 
frequently all three species breed and die. 

I conclude by saying something about the implications of this 
kind of work for the concept of programming. It is an adage 
(attributed to Lady Lovelace in the nineteenth century) that a 
computer does exacdy what it is told to do, neither more nor less. 
But a cjeep ambiguity inherent in this statement becomes apparent 
if one compares the two turtles moving around a square box, one 
following a geometric and the other a cybernetic program, that 
were mentioned earlier. Are they doing exacdy what they were 
"told" to do? If "telling" means actually writing it expliddy in the 
program, then one could say that the geometric turtle was "told" 
to go around the box. What the cybernetic turtle was told, how- 
ever, looks very different; in fact, it might need some thinking to 
decide that its program would make it go around the box. There 
is a distance between what it was told and those aspects of its 
behavior that interest the programmer. In other cases the distance 
been program and result can be even greater. An example that is 
familiar to anyone who has done much Logo is the program that 
draws a circle by doing REPEAT 360 [FORWARD 1 RIGHT 1]. Was 

204 • The Children's Machine 

the turtle told to draw a circle? If one says yes, one must say that 
it was told this in a very odd way. 

Earlier, I made a distinction between dead reckoning, or blue- 
print programming, and pilotage, or emergent programming. In 
the next chapter I shall use the language of blueprint and emer- 
gent programming to talk about economics and other "systemic" 
situations. I think it will appear that experience in the kinds of 
work discussed in this chapter will prepare young minds for the 
issues discussed there. 


What Can Be Done? 

WHEN one is overwhelmed, as everyone must be from 
time to time, by a sense that School is too firmly im- 
planted ever to change, it is helpful to contemplate the 
political changes across the globe that were until recently consid- 
ered quite impossible. The events in what we used to call the 
Soviet bloc are the most dramatic, but developments in South 
Africa, Chile, and Central America are in the same class. 

The sight of crowds demolishing the Berlin wall, or of Nelson 
Mandela sitting at a negotiating table with Frederik de Klerk, is a 
potent antidote to any tendency to say, "It can't happen." But the 
way these things did happen is sobering as well as heady. A closer 
look carries many lessons about the pain and difficulty of chang- 
ing a large, stable, well-rooted social structure. One of the most 
important of these is about how a system defends itself against 
recognizing the depth of its problems and the need for fundamen- 
tal change. 

Mikhail Gorbachev, whose name has deservedly become em- 
blematic of change, is also one of history's most interesting exam- 
ples of resistance to change. Even as he ushered in previously 

206 • The Children's Machine 

unthinkable reforms, he continued to pay allegiance to the ideas 
on which the system was founded, and renounced the Commu- 
nist party only when he was on the verge of being renounced 
himself. His slogan of perestroika (which literally means "restruc- 
turing") became synonymous with a policy of struggling to reform 
a system in serious crisis without calling in question the founda- 
tions on which it was built. It should be clear by now that I see 
most of those who talk loudly about "restructuring" in education 
in much the same light— though few of them have the courage to 
carry the reforms as far in their realm as Gorbachev did in his. In 
their case a more appropriate phrase than "restructuring" might be 
"jiggering the system." 

The analogy between perestroika and education reform would 
be instructive even if it went no further than highlighting these 
general features of change and resistance to change. But there is 
more. Using the language of system dynamics developed earlier, 
the problems of both the old Soviet Union and School can be 
described in terms of a conflict between tightly and emergently 
programmed systems. 

One of the key arguments used to justify the command econ- 
omy is that a tighdy programmed, highly planned economic sys- 
tem would necessarily be more efficient than one that operates 
though myriads of individual, uncoordinated decisions. In the 
Soviet Union this philosophical position was translated into a vast 
organization known as Gosplan, whose task was to program the 
entire economy in the tightest possible way. Every detail of every 
product was included in a master plan. For example, the plan 
would decree how many nails would be produced in the entire 
Soviet Union, where they would be made, how they would be 
distributed, and at what price they would be sold. The planners 
would know how many nails to make because they also decided 
how many would be made of each product that used nails. What 
was true of nails was true of everything else, resulting (theoreti- 
cally) in a fully rational economy with no waste -how much 
more sensible, it was argued, than the chaos of the capitalist 

What Can Be Done? • 207 

market economy, where every Tom, Dick, and Harry could decide 
to make nails, or not to make them. 

We encountered this same argument earlier, in the case of the 
"cathedral model" for education. The construction of a great 
Gothic cathedral (or any other large building) is a process that 
does require tight programming. It is not plausible that a cathe- 
dral would emerge from allowing workers to take independent 
actions of carving and placing blocks of stone. Careful p anmng 
by a skilled architect is obviously needed. The cathedral model 
for education applies the same principle to building knowledge 
structures. The curriculum designer is cast in the role or a 
"knowledge architect" who will specify a plan, a tight program, 
for the placement of "knowledge bricks" in children's minds. 
This is not very different from the argument for a Gosplan ap- 
proach to economics. 

Throughout this book 1 have developed concrete examples and 
abstract arguments to show that the Gosplan/cathedral form of 
tight programming is wrong as a general approach to education. 
The earlier discussion of blueprint programming and emergent 
programming supported this position indirectly by showing that 
even in simple physical situations, the argument for the advantage 
of precise blueprint programming is not universally valid. Some- 
thing as simple as programming a turtle to circumnavigate a rec- 
tangular box was easily done using an emergent approach, while 
it was difficult or even impossible to achieve by the blueprint 
method The failure of the Soviet-style command economy adds 
one more nail to the coffin of the idea that this method is ulti- 
mately superior. Important cases where some element of blue- 
printing is essential are the occasional exceptions rather than the 
model for how a project should be carried out. 

One cannot argue that the Soviet failure proves that a command 
economy cannot work, since its particular implementation was 
associated with so many other socially destructive policies. How- 
ever specific flaws in the operation of the system do suggest holes 
in the argument for its ultimate rationality. Consider the following 

208 • The Children's Machine 

schematic version of a kind of situation that had become endemic. 

The Ilyanova factory was required by the plan to produce 100 
tons of nails. The director had the idea of making oversized nails 
and produced 150 tons, so that he was rewarded with a bonus for 
150 percent achievement of the plan, even though nobody could 
use such large nails. It is really irrelevant whether the director's 
idea was brilliantly fraudulent or foolishly sincere; the absurdity of 
the system is brought out by the fact that every nail factory could 
fulfill its plan and at the same time there could be a national 
shortage of nails. 

Of course, under any system some people make fraudulent or 
foolish decisions. The relevant difference between the command 
economy and a market economy lies in the elbow room for other 
people to step into the breach: If the nail makers do not supply the 
nails for which there is a demand, sooner or later someone will 
realize that there is money to be made by creating a new nail 
factory. Thus initiative is widely distributed in the system and 
keeps it going through the operation of countless small and large 
feedback loops, working on the principles discussed in the previ- 
ous chapter. What is typical of emergently programmed systems is 
that deviations from what was expected do not cause the whole 
to collapse but provoke adaptive responses. 

I would not like to argue that we actually live in a fully sensible 
economic system — far from it. For many people the restrictions of 
poverty, prejudice, and our own forms of bureaucracy make a 
mockery of the concept of free enterprise. Even the economically 
powerful are constrained by limits to rationality. For example, the 
emphasis in American business on quarterly profits instead of 
looking at the real health of the company introduces an element 
reminiscent of judging success by counting nails. Nor would I like 
to argue that the Soviet system offered no opportunities at all for 
sensible initiatives; the fact that it survived as long as it did sug- 
gests that it did not fully conform to its own self-destructive ideal. 
Thus the comparison is not one of snow white and jet black. 

What I do want to argue is that while our economic system, 

What Can Be Done? • 209 

with all its faults, is above a threshold of functionality and theirs 
was below it, our education system falls on the same side of the 
line as the Soviet economy. We are living with an educational 
system that is fundamentally as irrational as the command econ- 
omy and ultimately for the same reason. It does not have the 
capacity for local adaptation that is necessary for a complex sys- 
tem even to function emciendy in a changing environment, and is 
doubly necessary for such a system to be able to evolve. 

What this means will be appreciated more concretely by look- 
ing at proposals for education reforms that fail in systemic think- 
ing. A good example is the plan with the grandiose tide "America 
2000," announced by George Bush so as to make good on his 
campaign promise to become "the education president." My dis- 
cussion is not intended as a partisan attack on Bush; the flaws in 
thinking are, in more or less severe forms, almost universal in 
contemporary educational thinking. 

The Bush plan was extraordinarily reminiscent of the Soviet 
style of "solving" problems by decree. Bush announced that by 
the end of the century American students will be the best in the 
world. The lynchpin of his proposals for achieving this was to 
institute a national system of tests. If this happened, he seemed to 
hope, Americans would no longer have to be embarrassed by 
reading that their children scored seventeenth in an international 
survey of science knowledge, or wonder whether there is after all 
any truth in the statement made by a Japanese politician in 1992 
that American workers are lazy and ignorant. He could point to 
our schools' productivity in test scores as the Soviet propagandists 
could point to their economy's output of nails. 

Denning educational success by test scores is not very differ- 
ent from counting nails made rather than nails used. There was 
no hint in Bush's education plan of any specific theory of what 
might be wrong with the present situation on the level of under- 
lying mechanisms. His remedies were the remedies the bureau- 
cratic mind proposes indiscriminately for every situation: Issue 
orders; tighten controls. Weakness in results can mean only 

210 • The Children's Machine 

that people are lazy and that a good system of tests will ex- 
pose them. 

But we can learn better by looking, for example, at Maria, the 
girl who placed the flashing light in her Lego house. She was 
certainly typical of contributors to the low U.S. rating on interna- 
tional tests. Quite likely she still is: It is improbable that her iso- 
lated experience with Lego-Logo did more than provide a hint at 
how she might develop first a taste and then an intuitive sense for 
things scientific and technological. Of course, the experience may 
have planted a seed for future development, though even if this 
were so I would not be at all sure that the change would show up 
as a higher score on a national test of science knowledge. In any 
case, whatever good came of the experience had little to do with > 
whether there is or is not a national test; it had everything to do 
with giving her an unusual opportunity to develop a healthy 
personal relationship with science. 

Indeed, if testing of the kind that Bush seemed to have in mind 
did have any effect on Maria at all, it would be negative. At least 
three different mechanisms would contribute to this. Nervousness 
about being tested on subjects that feel alien is the surest way to 
turn off what little interest a girl like Maria might have in science. 
On a more substantive level, tests would reinforce in her a very 
wrong and distasteful image of science as a list of facts to be 
memorized like a ritual. Furthermore, Maria would not be the only 
one to be influenced in these ways: Nervousness about the test 
could make the teacher reticent about spending time on any but 
the testable aspects of science. 

What would draw Maria and millions of others like her toward 
science, however, is offering them broader opportunities to ap- 
propriate it in a personal way. As such new opportunities are 
developed, it will be valuable to develop means to allow students, 
parents, and teachers to get a sense of how they are doing. Per- 
haps this will be called "testing," though the connotation of that 
word is so bad that something better should be invented. But 
whatever it is called, such a feedback mechanism must come in 

What Can Be Done? • 211 

the wake and not in the lead of new approaches to learning: 
A system of tests based on old models of learning will at 
best reinforce those models and inhibit the development of new 

Suppose — since there is no point in even thinking about re- 
forming education if we preclude success — the United States 
were to take a global lead in developing an approach to science 
education based on systems theory, or on allowing each child to 
become deeply involved in one personally selected branch of 
traditional science. Suppose also, as would be likely, that even if 
one or two countries were to join us or be ahead of us, most 
countries would lag behind and continue in the old paths. Under 
these conditions, our children might well rank poorly in interna- 
tional competition on old-fashioned tests: If the tests are inherited 
from the past or imitated from the rest of the world, they will 
inhibit us from moving forward except at the pace of the rest of 
the world. In fact, this might well mean not moving at all, since a 
change may have to reach a critical size in order to take place. The 
way to be £rst, therefore, is not to play catch-up but to take the 
lead in new directions. 

This is not to deny the need for a system of indicators of how 
well things are working. What was wrong with Bush's plan is that 
the test is not part of a self-correcting mechanism. Consider, for 
example, the light-seeking turtle. It used the principle of negative 
feedback, which by its nature implies some indicator of deviation 
from an intended state. Indeed, the key idea in designing the turtle 
for emergent programming was the selection of a suitable indica- 
tor. The design discussed in the text rejected the more obvious 
indicator of actual distance from the light in favor of the less 
"exact" indicator of deviation to left or to right. This indicator did 
not reflect how much progress had been made, but it did show the 
direction to go in order to make more progress. likewise, any 
teacher watching Maria would have easy access to such an indica- 
tor and could put it to much better use than a measure simply of 
how much science the student knows. The teacher would see that 

212 • The Children's Machine 

Maria was becoming engaged with a particular corner of technc, 
logical work and could conclude that she should be encouraged 
to go further in that direction. Indeed, Mana could draw this 
Idusion herself. Ttie educational flaw die 1 not come 
lack of indicators of directions to take but from the fact that S^ool 
provided only one direction and perforce she took «• After her 
fnZdual experience she went back to the impersonahty of the 

"Tame way, in the case of the naU 
system and the market system both use an ™f»™^loZ 
duction-a test. In one case the test measured conformity to the 
plan and we saw how that worked in a situation that is not as 
« as it might seem. In the other case the test is the pnee o 
nails which would respond to a shortage by going up and thus 
encourage producers to make more nails or potential producers to 
mmP into the nail business. 

Tanking abou, tests points up the real probta o our 
educadon system: the lack of flexibinty in 
spouses to what appropriate teats might reveal. The problem ta 
hreak awav from School's uniformity. 

"00, the plan proposed by the Bush ac— on pro § 
vides insight into how not to think about the issue. Bush and his 
lasers were, of course, committed to mouthing a 
capitalism and free enterprise, so it is not surprising that their plan 
was landed with talk about choice and competition and oppor 
.unities for initiative. But they were even more deep y omrnitted 
to maintaining the status quo, whatever it may bej So m the ^end 
their talk of choice became reminiscent of Henry Ford s pttcn 
abTut his Model T: You can have it any color you like as long as 
tfTbLck. They were further blinded to the possibility of change 
m eduction by their commitment to hierarchy-in orgaruzauon 
n epLemology , and in social relation. But calling hierarchy into 
question is the crux of the problem of educational <*™** 
" Bush's blindness to the real issues was visible m hi propo^ 
to make a grant of a million dollars to each congressional district 

What Can Be Done? • 213 

in support of an experimental school. At first blush this seems to 
£2ed a fosterinrdiversity, but it is predictable that the schools 
SleTd would be to the liking of the educational establishment, 
r n rln any case would not be sufficiently well funded to try 

„,,,„,llv work is a competlrion to select fifty proposals for expen 
rn"is and givTeach a grant of ten milkon dollars, with 
Z ludi under orirs to encourage diversity. Since the panel of 

u^s would * domiMted " y e , dUCa,,0 ,„ rSnor 

„, . would exnect the first ten or twenty choices to be minor 
%£^££Z we know it. But long before the panel go, 
„~hchoice, i, wouldbe forcedbyi* — 
pla „s that were really different. This variant, however * only * 
Light experiment to bring out the weakness of the Bush plan. 
bT£ from what I see as the likely route to mega- 
ch^e . on the contraty, this would have to begin much cloaer to 
the grass roots. 

To create a concrete image of change, imagine an ejemenmy 
LhooTteacher let's call her Martha, who reads this book and 
££t£e would like to follow Talma's example in her 
own classroom. Her first problem is to get some equipment Ten 
vears ago this would have been a main financial probletn n 
Cr ease there was a program that provided computers to 

atin a g teacher, other teachers wrote j£ 
suaded the school administration, or appealed to parents. But tor 
Martha School's "immune response" has created a different kind 
of^roblem. It is hard for her to get computers because her schoo 
haLlready invested heavily in them and is using ^-the 
purposes-perhaps for drill and pracuce, perhaps for computer 

^let us suppose that Martha has solved the equipment 
problem and is ready to move into action. She now faces an- 
£ problem, of acquiring a sufficient computer culture to feel 

214 • The Children's Machine 

confident about guiding her students. Many teachers in Thelma's 
generation participated in programs whose goals were not 
merely to provide technical knowledge about computers but to 
do so in the mathetic spirit that comes through in the vignettes 
of work in their classrooms. Martha will not find it easy to repeat 
their learning experience. She will have trouble finding a suit- 
able program. If she finds one she will have trouble convincing 
her school administration that she should be given the free time 
needed to participate in it. The administrators will draw her at- 
tention to the fact that the school system, or perhaps its com- 
puter vendor, provides seminars on "using computers." In a few 
afternoons teachers learn the essentials of computer literacy. 
You don't really need a three-week course. Besides, the school 
has a full-time computer teacher. The administrators at first don't 
understand her explanation that she wants to do much more 
than use a computer. But if Martha succeeds in getting the idea 
across that she is hoping to see children learn math in new 
ways, she will run up against a new obstacle. She is told that the 
school has already decided how children should learn math, that 
it has adopted the XYZ math series, that the district employs a 
math coordinator to discuss problems, that it is not for her to 
strike off on new initiatives of her own. 

Believe me, this barrage of objections is only a small part of 
the troubles Martha will encounter in attempting to launch her 
initiative within her school. What is remarkable is that many like 
her will actually manage to introduce new methods into their 
classrooms, though at the cost of dissipating in struggles with 
the system a large part of the extraordinary fount of energy that 
caring teachers find in themselves. The problem of channeling 
this energy more effectively is at the heart of my opening ques- 
tion; What can be done? It is not my intention here to provide 
a blueprint answer, for I neither believe that there is only one 
nor accept the idea of being in the position of a supplier (a 
"guru") to consumers of plans for change. What I shall try to do 
here is to place myself, as far as I can, in Martha's shoes and 

What Can Be Done? -215 

think through one example of a concrete plan, as Martha herself 
might do. 

Martha has come to the conclusion that there must be a better 
plan than tackling the obstacles one at a time. As long as she is an 
isolated individual in a school of forty teachers and three adminis- 
trators, such problems will come up over and over again. She 
believes that she would have the strength to continue to deal with 
them if there were no other way but has now decided to look for 
a more systemic approach. Looking around for models she finds 
three. A first approach, with Project Mindstorm as a model, is to 
"convert" the school, restructuring its ways of thinking and its 
forms of organization, not necessarily to conform fully with her 
own personal vision but sufficiently to provide space for a process 
in which she can believe. A second approach, based on models 
like the Costa Rican computer project, is to create a community 
that cuts across the boundaries of schools. A third approach, on 
which I will concentrate here, is the "little school" model— a 
name that comes from the Danish practice of providing govern- 
ment funds to groups of citizens who show themselves to be 
serious about setting up what in the United States we would call 
an alternative school. 

Martha has read about exciting little schools in Denmark but is 
able to find out more about models closer to home. In 1968 New 
York City carried out a formal decentralization of its school system 
by establishing school districts with a large degree of autonomy 
over the elementary and junior high schools in their territories. In 
itself this decentralization remained "formal" and did not give rise 
to any of the benefits that would come from a true break with 
centralized organization, largely because it was conceived as reor- 
ganizing the centralized bureaucratic system: The districts did not 
see themselves as challenging centralized authority as such; they 
saw themselves as acquiring a centralized authority over their own 
turfs. More recently some of the districts have adopted a policy 
that takes a more significant step toward a truer decentralization. 
They have set up a procedure to allow a group of teachers, gener- 

216 • The Children's Machine 

ally between six and ten, to submit a proposal to create a separate 
school with the right to set its own educational policy within 
guidelines approved by the district's school board. 

The little schools are still not examples of megachange. But 
Martha is not looking for a way to achieve megachange directly. 
She can see that the development of a megachanged learning 
environment will have to be a social process that will grow slowly 
in an organic way. It will involve the growth of a truly different 
culture of learning, replete with a literature, with jokes, with new 
ways of thinking about what is to be learned and how to learn 
it — in short, with much more than Martha and a handful of col- 
leagues can bring about by themselves. The problem she is trying 
to solve is on another level from making megachange: She is not - 
looking for a way to invent megachange single-handed but to 
participate in its emergence. She is looking for a way to lead a 
satisfying life as a teacher and, given who she is, this implies being 
part of the development of new ways of learning. 

In discussing Costa Rica I noted the way in which Logo became 
a medium for what Bell Hooks, writing about a similar situation 
in the experience of African- American women, called the recovery 
of identity. Work with computers became a way for people in a 
small "underdeveloped" country to lay claim to the tools of the 
future; it was a way for teachers to reject the definition of their 
profession as excluding the mastery of anything complex, mod- 
ern, and technical; and it was a way for women to declare to 
themselves as much as to others that technology was not some- 
thing that only men could own. In the United States I have seen 
Logo used by women in a similar spirit. I have seen children in 
"special ed" classes use it militantly to assert their real identity 
against School's classification of them as incompetent. Each of 
these cases suggests ways in which a little school created in a 
militant spirit can mobilize technology as an assertion of identity. 

In discussing intellectual styles I noted how bricoleurs were 
able to recover a particular kind of identity for which they usually 
had no name: an epistemological identity, which they had come 

What Can Be Done? • 217 

to feel was inferior and now found to be a source of intellectual 
power and pride. I am led to reflect on the fact that while many 
alternative schools define themselves by a domain of interest such 
as art or writing or science, few explicitly define themselves by an 
epistemological preference. 

The nearest approach I know to this is the Afrocentric school. 
Of course, in this case there is much more than an epistemology; 
there is a set of values, a sense of ethnic identity, and perhaps a 
political position. The one I know best is the Paige Academy in 
Boston, which adds yet more dimensions through its connections 
with the surrounding community. 

I could continue in this spirit, but this may be enough to make 
the point that little schools could give themselves a deeper and 
more conscious specific identity. Everything I have said in this 
book converges to suggest that this would produce rich intellec- 
tual environments in which not only children and teachers but 
also new ideas about learning would develop together. It is only 
in such an ecology of mutations and hybridizations of ways of 
learning that a truly new mathetic culture could emerge. As Dar- 
win taught us to understand, two key ideas that explain biological 
evolution and many other emergent processes are variation and 
selection. Although we now know that the process is more com- 
plex than Darwin imagined, biological evolution is still seen as 
dependent on there being ample opportunity for variety. I see 
little schools as the most powerful, perhaps an essential, route to 
generating variety for the evolution of education. 

The prevailing wisdom in the education establishment might 
agree with the need for variety but would look to other sources to 
provide it. For example, many— let us call them the Rigorous 
Researchers — would say that the proper place for both variation 
and selection is in the laboratory. On their model, researchers 
should develop large numbers of different ideas, test them rigor- 
ously, select the best, and disseminate them to schools. 

In my view this is simply Gosplan in educational disguise. 
Imagine that you had invented a new device for the kitchen and 

218 • The Children's Machine 

could demonstrate that ten million people wanted the thing. You 
would not be able to beat off the rush of would-be backers! Your 
device would soon be out in the world. Now imagine that you had 
an idea about education that appealed to twenty or thirty million 
people — say, to one person in five in every district of the country. 
Although in many areas of economic competition this would 
represent a market share beyond the wildest dreams of most 
entrepreneurs, it still might not be enough to generate a single 
"sale" to a school board. 

The ridiculous situation where supply and demand exist but 
cannot meet comes from the commitment to uniformity in 
schools. In most countries the uniformity works at a national level: 
A ministry of education would have to decide to adopt the new 
idea. In the United States there is a decentralized system that 
allows each town to make its own decisions. This makes it easier 
for some kinds of variety to exist: most easily, educational forms 
that match the social and class composition of a particular town. 
But variety on fundamental educational issues is just as effectively 
stalled by the requirement of majority assent on the level of a town 
or even of a school as on the level of a nation. The importance of 
the concept of the little school is that it provides a powerful, 
perhaps by far the most powerful, strategy to allow the operation 
of the principle of variation and selection. 

The Rigorous Researcher will object to the populist tone of this 
argument. It is appropriate to buy a food processor or a garlic 
press on the basis of individual whim, but education is more 
serious. Every child deserves the best. Science should be used to 
find out what is the best, and then everyone should adopt the 
proven methods. Personal decision is simply not appropriate. 

This objection depends on an assumption that is at the core of 
the technicalist model of education: Certain procedures are the 
best, and the people involved can be ordered to carry them out. 
But even if there were such a thing as "the best method" for 
learning, it would still only be the best, or even mildly good, if 
people (teachers, parents, and learners) believed in it. The bureau- 

What Can Be Done? • 219 

crat thinks that you can make people believe in something by 
issuing orders. This belief is supported by the rationalist, who 
believes that you can make people believe in something by 
advancing convincing arguments. But what if you can't? What if 
teachers and parents, and even children, persist in having different 
ideas? Then we have the choice of using force to run the system 
bureaucratically or reducing it to the common denominator of 
what everyone can believe. We would have totalitarian education 
or trivialized education. Indeed, if it were not for the resistance of 
teachers like Martha, School would not even make the choice 
but would achieve both — and sometimes it does so despite the 

A central feature of the little school idea is that it permits a 
group of like-minded people — teachers, parents, and children — 
to act together on the basis of authentic personal beliefs. Instead 
of imposing a common way of thinking on everyone, it allows 
people \vith a shared way of thinking to come together. I want to 
argue that this makes sense even from the point of view of the 
Rigorous Researcher, who should see that the little school is the 
most appropriate laboratory for the evolution of methods of learn- 
ing. This is true, in particular, of a component of children's learn- 
ing environment that has been given the least attention in this 
book, namely, parents. 

If Martha and her team are really going to explore new ideas, they 
are likely to act in ways that may go against the grain of how 
parents think about learning. This is something that can under- 
mine the effectiveness of the little school's work; but if parents 
understand what is being done at school, supportive discussion at 
home can very much reinforce it. So the match between parents 
and the school is also an important factor in how it will develop. 

An instructive example of the effect of unfavorable reactions of 
parents was provided by the "new math" movement that began in 
the 1960s. The launching of the first earth satellite by the USSR 
provoked a panic about Soviet superiority in science and technol- 

220 • The Children's Machine 

ogy , and this predated ; ^££ZZtZ£ 
TJ S schools that eventually spread all over me ; . 

mathematics in elementary school, learn lhc 

s<s p — r^e — 

placed too much emphasis ™£^™J£Z*J** 
that the remedy was to teach the cl* hen the g ^ 
mathematics. The argnmenl ™ i deeply ^lawe 
waySi of which the most 

general public, and that tncluded th i vaa MW«? P 
5* undersranding of ™* Lit 

lt . Many parents «*^^'^« w » Jrning. And 
children doing-hardly a good way to 7 wtatthelrch ||dien 

"IrmpSnce of parent ^onstonva*^^ 
the ^ and 

educational change, lt also htgni tg ■ movement fail 

neg^Wed^Noto^ten^r^^ ^ ^ 

to please parents, but the instigators . ions prece d- 

even consider this to be «^££££S much 
tag the design and '^r^*,,,, about wha , kind of 
attention to J "^^tSCS*- - 
^^S^t^Tb, chifdren. The 

ItZion at al, to ^h orTtae 
sider questions about the relauonsnip 

comes. At the least, more attention would have been pat 

What Can Be Done? • 221 

helping parents understand what was being done. It is hard to 
prediefwhat would have happened in this case. Certainly the 
response to the new approach would have been somewhat more 
enthusiastic. In my view it would not have been very much more 
so because the conflict between the culture and the new math 
was too deep to be overcome by good public relations. A more 
significant possible consequence could have been that the in- 
novators might have come to understand the need to redesign 
their curriculum to obtain a better cultural resonance. But in either 
case the story of the new math has a moral for Martha and for 
those trying to support her efforts: The design of a learning envi- 
ronment has to take account of the cultural environment as well, 
and its implementation must make serious efforts at involvement 
of the communities in which it is to operate. 

I am not sure that any approach to math reform could have 
been effective in the 1960s. Fortunately, Martha lives at a time 
when many factors contribute to richer opportunities for develop- 
ing a culturally syntonic learning environment. It is instructive for 
the general problem to review some of the ways in which mathe- 
matics can be handled better by little schools that might provide 

a model for Martha. 

One must never get tired of reiterating the obvious: Even if 
nothing else had changed, the simple fact of being a little schoo 
could make a decisive difference if it led to a self-se ectton of 
parents who were favorable to its particular educational philoso- 
phy in that case, instead of struggling with a skeptical and dis- 
trustful parent body, the school would benefit from the commit- 
ment the parents made in selecting the school. Even at the time of 
the new math movement, an alternative school could have used 
this factor-and, indeed, some did-to create a better intellectual 
ambiance. But today a little school can take this advantage much 
further The particular innovation made in the new math was 
isolated in various ways. It was confined specifically to math with 
a little spillover to science; it was in its nature attractive to a small 
number of people. 

222 • The Children's Machine 

Building its approach to mathematics on the use of computers 
gives the modern littie school a chance to break out of this isola- 
tion. Quite independendy of its "true" educational value, associat- 
ing mathematics with computers has a much better chance to elicit 
positive responses than associating it with an unknown esoteric 
thing called "set theory." A typical parent's reaction will be much 
more positive to a child coming home and saying, "I did math 
with computers," than to, "In math we did set theory." This kind 
of acceptance of the computer is open to exploitation: All sorts of 
superficial activities are dressed up as "computer learning." But 
the fact that poor educational methods can be dressed in compu- 
tational clothing does not in any way diminish the fact that a 
favorable attitude to the idea of children learning about computers 
can be used as a bridge for parents to understand educationally 
sound work. The parents are predisposed to hear. They are also 
predisposed to believe that learning about computers leads to 
learning about mathematics, for it is well established in the public 
mind that computers are "mathematical." People might not quite 
know what this means, but it is enough to establish a positive 
attitude to mathematics through the subject's connection with 

A new approach to mathematics through computation reduces 
isolation in other ways as well, for, as I have repeatedly shown in 
this book, mathematics is thereby connected with many other 
domains of interest that parents might understand and care about. 
This includes specific subjects such as dance, robotics, writing, 
and social studies; but perhaps even more important, it includes 
epistemological positions that might appeal to parents through 
feminist, Afrocentric (and other kinds of multicultural), or envi- 
ronmental connections. Thus there is a basis in principle for the 
little school to try to develop dialogue with parents on a range of 

Of course, there is a big step between the existence in principle 
of a basis for dialogue and its establishment in a rich form. I am 
not trying to suggest that this is easy or even that I know how to 

What Can Be Done? • 223 

go about it. My point is simply that a very new opportunity exists 
for mobilizing a larger public in pursuit of educational change. 
And it seems to me very clear that a dynamic little school that is 
itself based on a principled stand on the connecting issues is in a 
much better position to do this than a cumbersome traditional 

Another way in which technology will contribute to providing 
a more favorable environment to the diverse initiatives toward 
new contexts for learning is through electronic communications. 
Even if there were many more little schools than exist today, and 
even if they were bolder and more varied in their innovations, they 
would not constitute an evolutionary ecology unless they were 
pan of an interacting system. The development of better technolo- 
gies of communication has a significant contribution to make to 
thevtransformation of the command system of School to an initia- 
tive system. 

New technologies of communication also provide an answer to 
what some readers might have seen as an objection to the concept 
of little schools. They might seem to be isolationist, fostering a 
greater balkanization of communities than exists already. But 
imagine being able to visit electronically with a school in a virtual 
reality similar in spirit to the virtual reality in which I was imagin- 
ing Jennifer visiting giraffes in Africa. Imagine schools from across 
the world collaborating on projects. Such images suggest oppor- 
tunities for contact among schools that go far beyond anything 
known in the past. It is no longer necessary to bring a thousand 
children together in one building and under one administration in 
order to develop a sense of community. 

This, in turn, means that over time the function of little schools 
is likely to change. The large schools are too cumbersome to 
maneuver in the turbulent waters of megachange. My vision is not 
inconsistent with a scenario in which a little school's movement 
draws in 10 percent of the children, uses this to blaze a trail toward 
new ways of learning, but passes out of existence when this 
catalytic and exploratory function has been served. Yet I do not 

224 • The Children's Machine 

see this as the most likely scenario, for over the long run it is 
probable that large schools will cease to be needed at all. 

What advantage does the large school have over the little one? 
Some advantages that existed in the past are destined to vanish. 
This is most strikingly true of the ability to afford a large library. 
Few schools have good libraries anyway; but in the electronic era 
every school, indeed every home, will be able to have distant 
access to reference books, encyclopedias, and the like, as well as 
the world's literature without the reader's having to move from 
armchair or playroom. Likewise, communication technology will 
expand the opportunity to meet other people of like interests. 
Even the always more or less illusory belief that in a large school 
there is a better chance to have a teacher in whatever area might 
interest an individual student is undermined by the possibility of 
getting in touch with experts at a distance. 

There is only one kind of argument against little schools that 
troubles me, though not sufficiently for me to abandon the ap- 
proach. These arguments turn around issues of elitism and of 
protecting children from exploitation. In principle, the traditional 
public school has the potential of ensuring equal opportunity for 
everyone. In principle, the idea of breaking it up into smaller units 
undermines, if not the potential for protecting children, at least the 
traditional ways of trying to do so. 

In the last analysis my answer to these arguments is that public 
school has paid the heavy price of bureaucratization without ade- 
quately protecting those in greatest need. In this sense there is no 
substantial objection to answer. The situation once again evokes 
an analogy with the Soviet economy. The USSR used to boast that 
all its citizens had jobs and a degree of social security. It pro- 
claimed that it protected everyone. But a terrible price was paid, 
and not in fact for protection but for the illusion of protection. 1 
do not see that School can be defended in its social role. It does 
not serve the functions it claims, and will do so less and less. 

These functions of social protection of children are certainly 
needed. It would be heartbreaking to look into the future only to 

What Can Be Done? • 225 

see wonderful networks of access to knowledge for some people 
while others were excluded, or to see that education had become 
even more than in the past a breeding ground for intolerance and 
hatred. The prospect is so grim that I would be reluctant to accept 
any merely intellectual advantages at the cost of giving up a status 
quo that served democracy and cultural diversity. But what I am 
not ready to accept is giving up real advantages in exchange for 
the pretense of equality. The only rational choice I see is to forge 
ahead in the encouragement of educational diversity with a dedi- 
cated commitment not only to expanding its benefits to all who 
want them but also to making sure that those who choose not to 
want them are making an informed choice. 

Sources of Information 

Council for Logo in Mathematics Education 
10 Bogert Avenue 
White Plains, NY 10606 
Phone; (914) 946-5143 

Epistemology and Learning Group 
Media-Lab E15-309 

Massachusetts Institute of Technology 
20 Ames Street 
Cambridge, MA 02139 
Phone: (617) 253-7851 
Fax: (617) 253-6215 

Logo Foundation 

250 West 57th Street, Suite 2603 

New York, NY 10107-2603 

Phone: (212) 765-4918 

Fax: (21 2), 765-4789 

Logo Special Interest Group 

International Society for Technology in Education 

1787 Agate Street 

228 » Sources of Information 

Eugene, OR 97403-1923 
Phone; (503) 346-4414 
Fax: (503) 346-5890 

Sources of Logo Software 

Harvard Associates 
10 Holworthy Street 
Cambridge, MA 02138 
Phone: (617) 492-0660 
Fax: (617) 492-4610 

Lego Dacta 
555 Taylor Road 
Enfield, CT 06082 
Phone: (800) 527-8339 
Fax: (203) 763-2466 

Logo Computer Systems, Inc. 
P.O. Box 162 

Highgate Springs, VT 05460 
Customer Service: (800) 321-5646 
Fax: (514) 331-1380 

Paradigm Software, Inc. 
P.O. Box 2995 
Cambridge, MA 02238 
Phone: (617) 576-7675 

Terrapin Software, Inc. 
400 Riverside Street 
Portland, ME 04103 
Phone: (207) 878-8200 
Fax: (207) 797-9235 


• • • 

Freire, Paulo and Donaldo Macedo. Literacy: Reading the Word and 

the World. New York: Bergin & Garvey, 1987. 
Illich, Ivan. Deschooling Society. New York: Harper & Row, 1983. 
Latour, Bruno. Science in Action. Cambridge: Harvard University 

Press, 1987. 

Lave, Jean. Cognition in Practice. Cambridge: Cambridge University 
Press, 1988. 

McCulloch, Warren. Embodiments of Mind. Cambridge, Mass.: MIT 
Press, 1965. 

Papert, Seymour. Mindstorms: Children, Computers, and Powerful 
Ideas. New York: Basic Books, 1980. 

-. "Teaching Children Thinking." In The Computer in the 

School: Tutor, Tutee, Tool, ed. Robert P. Taylor. New York: Teach- 
ers College Press, 1980. 

Peck, M. Scott. The Road Less Traveled. New York: Touchstone/ 
Simon and Schuster, 1980. 

Piaget, Jean. The Child's Conception of Number. New York: Norton, 
[1941] 1965. 

-. The Grasp of Consciousness: Action and Concept in the 

Young Child. Cambridge, Mass.: Harvard University Press, [1974] 

230 • Bibliography 

Resnick, Mitchel. "Beyond the Centralized Mindset." Ph.D. diss., Mas- 
sachusetts Institute of Technology, 1992. 

Suppes, Patrick. "The Future of Computers in Education." In The 
Computer in the School: Tutor, Tutee, Tool, ed. Roben P. Taylor. 
New York: Teachers College Press, 1980. 

Turkle, Sherry. The Second Self: Computers and the Human Spirit. 
New York: Simon and Schuster, 1984. 

Turkle, Sherry and Seymour Papert. "Epistemological Pluralism: 
Styles and Voices within the Computer Culture." Signs 16, no. 1 

Wiener, Norbert. Cybernetics: Control and Communication in the 
Animal and the Machine. New York: Wiley, 1948. 

. The Human Use of Human Beings: Cybernetics and Society. 

Garden City, New York: Doubleday, 1954. 


• • • 

Accommodation, 41 
ACE computer, 157, 158-59 
Aeronautics, 15, 28-29, 30, 86 
Aesthetics, 69-70, 119, 132 
Africa, viii, 6-7, 139, 151, 191, 

205, 223; textiles of, study of, 

17, 53-54 
Afrocentrism, 74, 217, 222 
"Aha" experiences, 38, 121-22 
AI (Artificial Intelligence), 165, 

166, 169-70,. 173, 175; and 

cybernetics, 182, 183 
Algebra, 13, 14, 159. See also 

America 2000 plan, 209, 211-13 
Androcentrism, 74, 150, 152, 

Animation, 46, 49, 71 
Anthropology, 150 
Apple computer, 35 
Appropriability, quality of, 191, 


Aptitudes, 63-64 

Arias, Oscar, 75, 77 

Art, 79, 148; and fantasy, 183; 
technology vs., cultural 
opposition of, 118, 123 

Artificial intelligence. See AI 
(Artificial Intelligence) 

Assimilation, 41 

Aviation, 15, 28-29, 30, 86 

"Banking model" of education, 

14, 51, 62 
basic, 160, 163, 171 
Bateson, Gregory, 192-93 
Behaviorism, 104, 164, 165 
Bill (case study), 43 
Biology, 68-69, 182, 202; and 
cybernetics, 190; etymology 
of the word, 106; and 
qualitative knowledge, 21; 
and technology, union of, 20 

232 • Index 

Bitzer, Donald, 160 

Blue-print programming (dead 
reckoning), 204, 207 

Body: and mathematics, 31, 
90-91; and "reasoning from 
within," 201; and robotics, 
53, 129; and thermostats, 
195-96. See also Dance 

Botany, 52, 73, 84, 93-105, 
113-14, 152, 180 

Brian (case study), 43-50, 54, 
61, 64, 67, 79, 126, 136, 140, 
145, 158 

Bricolage, 143-46, 152-53, 156, 
216-17; and cybernetics, 
200-201; definition of, 131, 
200-201; and proximality, 
concept of, 201 

Bureaucracy, viii, 60, 76, 78-79, 
208-10, 218-19, 224; and 
decentralization, 215 

Bush, George, 209, 211, 212-13 

CAI (Computer Aided 

Instruction), 41-43, 76, 107, 

Calculators, 161 
Capitalism, 206-207, 212 
Case studies. See Students (case 

Chemistry, 59-60, 61, 67 
Child-centered education, 14 
Children as Software Designers 

(Hard), 110 
Chomsky, Noam, 165 
Choreography, 26, 47, 61 
Class, social, 133, 136, 218 
"Clean learning," 134-36 

Coercion, 57-58 
Common sense, 27, 60, 138 
Communism, viii, 206. See also 

Soviet Union 
Competition, vii, 37, 212, 213, 


Computer Aided Instruction 
(CAI), 41-43, 76, 107, 163-68 

Computer in the School: Tutor, 
Tutee, Tool, The (Taylor), 

Computer labs, 39, 51, 53-54, 
66; and the Costa Rica 
project, 77; time available in, 

Computer literacy, definition of, 

Concreteness, concept of, 138 
Connectionism, concept of, 

Constructionism, 137-56 
Constructivism, 14, 17, 83, 104, 


Cooking, 30-31, 32, 55, 113-16. 

See also Kitchen math 
Costa Rica project (Programa 
Informatica Educativa), 
75-78, 110, 158, 215, 216 
Creativity, 33, 70, 167, 173, 183 
Croissants, 30-31, 32 
Cultivation, concept of, 104 
Cybernetics, 179-204; and 
"centralized mindsets," 
201-202; and feedback, 
187-88, 191, 192, 193-94, 
196; and gender, 198, 199, 
201; and "managed 
vagueness," 185, 189; and 
"reasoning from within," 

Index • 233 

199- 200, 201; and the turtle, 
185-91, 196-97, 201-202, 
203-205, 207 
Cybernetics: Control and 
Communication in the 
Animal and the Machine 
(Wiener), 181-82 

Dance, 11, 26, 44-45, 47-50, 

131-36, 222 
Data bases, 70 

Dawn (case study), 126-27, 140 
Dead reckoning (blue-print 

programming), 186, 189 
Debbie (case study), 38, 

107-113, 127-28, 131, 136, 

140-41, 145-46, 155, 158, 


Debugging, 52 
Decentralization, 215, 218 
Democracy, 6, 15, 225 
Descartes, Rene, 47, 85 
Deschooling Society (Illich), 141 
Desktop publishing, 23 
Developmental teaching, 40-41 
Dewey, John, 5, 6, 15, 16 
Dirty Dancing (film), 132-36 
Disabilities, learning, 38, 89~90, 

Discovery method, 16 
Distancing, 22 

Dumb, use of the word, 172 

Ecology, 161, 203, 223. See also 

Economics, 20, 37, 203-204; 

and command economies, 

206-208, 209, 212, 224 

Electronic mail, 37 
Electronic notebooks, 8 
Elevator code, example of 

learning, 63 
Emergent programming, 186, 

187, 189, 204, 207, 208, 211 
Environment, viii, 104, 180, 222; 

and the concept of feedback, 

20; and the Kidnet project, 


Epistemology, ix, 6, 16-17, 58, 
109, 212, 222; and the 
Afrocentric school, 217; and 
being "vaguely right," 
167-68, 172-73; and 
bricolage, 152, 216-17; and 
computerists, 164-65, 
167-68, 172-73; and 
constructionism vs. 
instructionism, 137, 145, 152, 
155-57; and cybernetics, 
182-85, 194; and feedback, 
concept of, 20; and 
hard-edged programming, 74; 
hierarchical theory of, 62; and 
kitchen math, 114-15; and 
phenomenon of, 63-64; and 
literacy, use of the term, 
10-11; "of precision," 185; 
and the primacy of reading, 
9; and science and aesthetics, 
69-70; and turning science 
into "used knowledge," 183 

Errors, 120, 187, 190 

Ethnic differences, 118, 124, 217 

Etymology, 96-97, 100, 

Evaluation, 71, 75 

234 • Index 

Evolution, 15, 27, 203, 217 
Exceptional children, 13-14, 

23-24; interaction between, 

44-45, 50 

"Factlets," 164 

Families", 20, 55, 125, 193, 

Fantasy, 20, 91, 183 
Feedback, 191-94, 196, 187-88, 


Feminism, 74, 80, 152, 164, 222 

Fernandez, Alejandrina, 75 

Feuerzeig, Wally, 171 

Feynmann, Richard, 180 

Film, 11, 132-36 

Flowers, 106, 107, 192; study of, 
52, 73, 84, 93-105 

Fluency, 48, 49 

Fonseca, Clotilda, 76 

Force: concept of, 199; use of 
the word, 138 

Fractions, 107-13, 140-41, 155, 
165; and bricolage, 144-45, 
146; and "clean learning," 
135-36; and kitchen math, 

Francisco (case study), 117, 118 
Frank (case study), 89-91 
Free enterprise, 208, 212 
"Free school," advocates of, 44 
Freire, Paulo, 10, 14, 51 
French language, 32, 64, 131, 

Freud, Sigmund, 91, 152 

Gardner Academy (San Jose, 
California), 78 

Gender, 13, 42, 76, 118, 163; 
and abstract-formal 
knowledge, emphasis on, 
148; and cybernetics, 198, 
199, 201; and Lego-Logo 
projects, 198, 199; and 
"reasoning from within," 201; 
and technology, attitudes 
towards, 119, 124 
Generality, ideal of, 143-44 
Geometry, 13, 176-78; and CAI, 
43-44, 47; and the Lego-Logo 
workshop, 119; and the study 
of African textiles, 17-19. See 
also Mathematics 
Gorbachev, Mikhail, 205-206 
Gosplan, 206-207, 217-18 
Gothic cathedral model of 

learning, 62-63, 207 
Grammar, 32, 83, 85, 173, 175 
Grey, Jennifer, 133 

Hard-edged programming, 73, 

74, 148, 159, 162 
Harel, Idit, 108, 110 
Hechinger, Fred, 59, 60-61, 67, 


Hennigan Elementary School 

(Boston, Massachusetts), 

50-51, 52, 68, 77 
Henry (case study), 43-50, 54, 

61, 64, 67, 79, 126, 136 
Heterarchy, concept of, 61-62, 


Heuristics, 85, 86-87, 89, 189 
Hierarchical organization, 

60-62, 65, 83, 184, 190, 212 
History, 13, 68 

Index • 235 

Hobbies, 13, 29-30, 35 
Hooks, Bell, 216 
How to Solve It (Polya), 85 
Humor, 91, 125-28, 172, 

IBM, 35, 75, 158 

Identity, 23-24, 29, 216-17, 

119, 123 
Illich, Ivan, 141, 144 
Illiteracy. See Literacy 
Imagination, 29, 34, 132, 183 
"fmmune responses," 50-54, 

Individuality, 22-24 
Individualized instruction, 41 
Information, access to, 45, 191 
Instructionism, 137-56 
Intuition, 27, 28, 58, 107, 165; 
and computerists, 158, 
166-67; and game-playing 
programs, 171; and 
Lego-Logo projects, 210 

Japan, viii, 35, 209 
Jeff (case study), 147-48, 150, 

Jennifer (case study), 6-8, 

9-10, 11-12, 191 
Joe (case study), 66-67, 69, 

Jokes, 91, 125-28, 172 

Kay, Alan, 36, 42 
Keller, Evelyn Fox, 152 
Kemeny, John, 160, 163 

Kevin (case study), 147-48, 

150, 178 
Kidnet project, 25-26 
Kinesthesia, 8, 31 
Kitchen math, 113-17, 131, 

141-43; and bricolage, 

144-45, 146; and 

constructionism vs. 

instructionism, 153 
Knowledge Machine, 8-9, 11, 

12, 13, 17, 191-92 

phenomenon of, 63-64, 65 

Lamplighter School (Dallas, 

Texas), 25, 77 
Languages, foreign, 32, 121; and 

aptitudes, concept of, 64; 

French, 32, 64, 131, 143-44; 

Latin, 58, 84, 96, 101, 103; 

and the use of the word 

fluent, 48 
Latin (language), 58, 84, 96, 101, 


Latour, Bruno, 150, 151 

Lave, Jean, 113 

Learning disabilities, 94, 95 

Learning stories. See Students 
(case studies) 

Lego, 87, 89, 122-24, 173; and 
bricolage, 144; and 
constructionism, 142; and 
cybernetics, 194, 197-99; lab, 
at MIT, 128-31; -Logo 
projects, 118-24, 144, 170, 
197-99, 210 
Leonardo da Vinci, 15, 28 
Lesson plans, 55, 59-60, 61 

236 • Index 

Letteracy, 16, 49; definition of, 

Levi-Strauss, Claude, 131, 
143-44, 150, 151-53 

Lift, principle of, 28, 29 

Linnaeus, 84, 97 

Literacy: "computer," 51-62, 
213, 214; definition of, 52; 
"flower," 93; and letteracy, 
11-12; and oral fluency and 
writing, contrast between, 49; 
use of the word, 10-11 

"Little schools," 215-17, 219, 
221, 222, 223-24 

Logic, 153, 157, 158; and 
artificial intelligence, 165; 
"bashing," 146; and 
computerists, 164, 166; and 
cybernetics, 182, 190; and 
intuition, 166-67; and New 
Math, 220; and the turtle, 187 

Tx>go, 20, 34, 45-46, 64; and the 
African textiles study, 17-18; 
and the Costa Rica project, 
76-77; and cybernetics, 
197-99, 201, 202; 
development of, 58-59, 171, 
173-74, 175-76; and "funny 
learning," 126; and the 
guidance process, 168; and 
the human skeleton, study 
of, 68-69, 70; and 
leaming-in-use, 64-66; Lego- 
projects, 118-24, 144, 170, 
197-99, 210; LogoWriter 
program, 68; Microworlds 
Logo version, 20; and PET, 
42; and Project Headlight, 
50-51; and Project 

Mindstorm, 78-79; and 
"reasoning from within," 201; 
and the "Robin Hood 
vision," 180; and studying 
fractions, 107-13; traffic 
program, 202-203; 
workshop, for teachers, 

McClintock, Barbara, 152 
McCulloch, Warren, 33, 61, 190, 

Maria (case study), 116-25, 

127-28, 131, 145, 210 
Market systems, 212 
Martha (case study), 213-14, 

216, 219 
Mary (case study), 177-78 
Matchstick game, 170, 173-75, 


Mathematics), 26, 31-32, 38; 
algebra, 13, 14, 159; and 
aptitudes, concept of, 64; and 
art, 79; and CAI, 43-44, 45, 
47, 165-66; and "clean 
learning," 135-36; and 
computerists, 157, 158, 159, 
165-66; and constructionism 
vs. instructionism, 139-40, 
146; education in, central 
problem for, and computers, 
16-17; and fact-oriented 
subjects, integration of, 68; 
and "funny learning," 
125-28; and "generalizing the 
idea," 46; Hindu, 126; and 
learning disabilities, 89-90, 
92-93; learning of, as a 

Index • 237 

foreign language, 64; and 
Lego-Logo projects. 198; 
origins of the term, linguistic , 
84; purposeful use of, 47-48; 
multiplication, 165-66; New 
Math, 140, 219-21; "oral," 
documented by Piaget, 16; 
and permissiveness, 124; and 
"set theory," 222; and the 
study of fractions, 107-16, 
135, 140-41, 144-45, 155, 
165; tables, production of, 
184-85; and waves, ideas 
about, 202-203. See also 
Kitchen math 

Mathetics, 84-87, 89~92, 97, 
104-105; and constructionism 
vs. instructionism, 137, 139, 
141, 143, 145; and kitchen 
math, 114, 115; and "little 
schools," 217 

Medicine, 1-2, 14, 55, 56, 103, 

Megachange, 19, 54-55; and 
the Bush plan, 213; and the 
history of aviation, 28-29; 
and intuition, 27; and the 
"little schools," 216; and 
Mindstorms, 35-36; and 
social evolution, 27 

Memory, 63; and the "banking 
model," 14, 51, 62; computer, 
159; and flowers, study of, 
93-96, 97-98, 102-103 

Mentalism, 143 

Metaphysics, 31, 194 

Microcultures, 73-74 

Microworlds, version of Logo, 

Mihich, Orlando, 54 
Military, 61, 157, 158, 179-82, 

184, 185 
Mindstorms; Children, 

Computers, and Powerful 

Ideas (Papert), 35 - 36, 40, 42, 

58-59, 84; display of 

aptitudes in, 63-64; 

geometric construction of 

houses in, example of, 73; 

use of "syntonic" in, 144; 

writing of, 36 
Minsky, Marvin, 33, 165 
Missiles, 179, 181, 182, 184, 185 
MIT (Massachusetts Institute of 

Technology), 8, 33, 74, 

77-78, 128, 166, 168-69, 171, 


Motivation, idea of, 94 
Multiculturalism, 222 
Multiplication, 165-66 
Music, 11, 26, 44, 48, 135 

Naming, 73-74, 93-105 
National Geographic Society, 25 
National Science Foundation, 45 
"Nation at Risk, A," (report), 37 
Nature, relationships with, 

101-102. See also Ecology; 

Navigation, 186-87, 188, 189, 


Negroponte, Nicholas, 8 
Neumann, John von, 184 
New Math, 140, 219-21 
Newspaper, as personal 

learning experience, 23—24, 

27, 29 

238 • Index 

New York City public schools, 

43, 59-60, 215-16 
Newton, Isaac, 149-50 
Nintendo, be, 87, 140 

Objectivity, 22 
Organizational forms. See 

Paige Academy (Boston, 

Massachusetts), 217 
Painting, 11, 61, 132, 183 
Parenting, 55, 125, 219-22 
Peck, M. Scott, 87-89, 92-93 
Pedagogy, 82, 139 
Pensee sauvage, 150, 151 
Personal computer, coining of 

the term, 42 
PET (Progressive Educational 
Technology) movement, 42 
Physics, 53, 131, 138, 160, 199 
Piaget, Jean, 139, 143; and Al, 
169; assimilation and 
accommodation in, 41; and 
behaviorism, 165; childhood 
of, 24, 25, 26, 110; concrete 
intelligence in, 138; 
exceptional intellectual 
qualities of, 24, 25; first paper 
published by, 24, 110; 
intelligence and the 
evolutionary process in, 15; 
"oral" mathematics 
documented by, 16; at the 
Sorbonne, 33; as the theorist 
of learning without 
curriculum, 54; theory of 

stages, 138, 151-55; thinking 
of young children in, 
vocabulary used to describe, 
74; on the "transmission" of 
knowledge, 142; "to 
understand is to invent" 
principle of, 34, 169 

Pilotage, and emergent 
programming, 186, 187, 189, 
204, 207, 208, 211 

PLATO system, 160 

Pluralism, 6, 81, 155, 157, 182 

Poetry, 61, 113, 116, 145 

Polya, George, 85-87 

Polymath, 84 

Printing, 23, 55-56 

Problem solving, 85, 86-89, 

Process learning, definition of, 

Programa Injbrmatica 
Educativa (Costa Rica 
project), 75-78, 110, 158, 215, 

Progressive education, 14-15, 

38-39, 40, 42, 63 
Project Headlight, 50-51, 77 
Project Mindstorm, 78, 79, 215 
Proximality, 201. See also 

Psychology, 21, 22, 27, 67, 160; 

and AI, 169; and 

constructivism, 142; and the 

dream of a science of 

learning, 149; and 

learning-in-use, 65; and 

"learning theory," 83 

Qualitative knowledge, 20-21 

Index • 239 

Race, 42, 163 
Raymond (case study), 38 
Reading and writing, 11, 49, 
183, 222; and learning 
disabilities, 92-93; and 
mathematics, 17; monopoly 
on, in the past, 34; primacy 
of, 9; and use of the word 
literacy, 10. See also Literacy 
Reasoning, "from within," 

199-200, 201 
Repression, 91, 152 
Resistance, 152 
Resnick, Mitchel, 201 
Resource rooms, 89-90 
Richard (case study), 50-51 
Ricky (case study), 128-31 
Rigorous Researchers, 217-19 
Road Less Traveled, The (Peck), 

Robotics, 118, 128-31, 157-58, 
163, 173, 175, 222; and 
cybernetics, 181, 182; project 
(Missouri), 53-54; and the 
"Twenty-one" game, 170 

Romeo and Juliet 
(Shakespeare), 132-33 

Ronkin, Joanne, 52 

Rosenblatt, Frank, 190 

Russia. See Soviet Union 

Satellites, 219-20 

Savage Mind, The (Levi-Strauss) 

Schoolers, 1-21, 34 
Science, 23, 124, 132, 143-45, 

167; and aesthetics, issue of, 

69-70; analytic, 144, 145, 150; 

and constructionism vs. 

instructionism, 144, 145, 149, 
150-52; and fantasy, 20, 183; 
and "funny learning," 127; 
the humanities and, cultural 
opposition of, 118; 
integration of, with 
mathematics, 68; knowledge, 
international survey of, 209, 
210; and Lego-Logo projects, 
198; and process learning, 
140; and qualitative 
knowledge, 20-21; and the 
scientific method, 26-27, 149, 
150; Soviet "superiority in," 
panic regarding, 219-20; 
success in, and luck, 128; 
transformation of, into "used 
knowledge," 183. See also 
Biology; Botany; Ecology; 
Evolution; Experiments; 
Second Self, The (Turkle), 

"Sesame Street" (television 

program), 154 
Sex differences. See Gender 
Sexuality, 89, 91-92; and "clean 
learning," 135; and dance, 
134, 135; repression of, 152 
Shannon, Claude, 190 
Shaw, George Bernard, 57 
Simon, Herbert, 172 
Simulation, 21, 35, 161 
Skeletons, study of, 68-69, 70 
Skiing, 47-48 

Smart, use of the word, 172 
Smart missiles, 179, 181, 182, 

184, 185 
"Smoky programming," 73-74 
Snow, C, P., 118 

240 • Index 

Social class, 133, 136, 218 
Social protection, of children, 

Soviet Union, vii-viii, 206-209, 
212, 217-20, 224; Gosplan in, 
206-207, 217-18 
Special education, 94, 216 
Speech, learning of, 12-13 
Spelling, 13, 32 
Sperry, Carol, 78, 79-80 
Students (case studies): Bill, 43; 
Brian, 43-50, 54, 61, 64, 67, 
79, 126, 136, 140, 145, 158; 
Dawn, 126-27, 140; Debbie, 
38, 107-113, 127-28, 131, 
136, 140-41, 145-46, 155, 
158, 165; Francisco, 117, 118; 
Frank, 89-91; Henry, 43-50, 
54, 61, 64, 67, 79, 126, 136; 
Jeff, 147-48, 150, 178; 
Jennifer, 6-8, 9-10, 11-12, 
191; Joe, 66-67,69, 72-73; 
Kevin, 147-48, 150, 178; 
Maria, 116-25, 127-28, 131, 
145, 210; Martha, 213-14, 
216, 219; Mary, 177-78; 
Raymond, 38; Richard, 50-51; 
Ricky, 128-31; Thelma, 43, 
45-46, 62, 64, 66-67, 213, 

Subject boundaries, 39 
Suppes, Patrick, 160, 163-64, 

166, 167, 172, 184 
Swayze, Patrick, 133 
Systemic effects, 53 
Systems theory, 203, 211 

Taboos, 89, 91-92 
Taylor, Robert, 161 

Teacher(s), 38-41, 50, 57-81, 
109, 214-16; and being 
precisely right, 167-68, 
172-73; and biased 
perceptions, 42; and the 
blinking light project, 
123-24; and CAI, 41; and 
"clean teaching," 134-36; 
"computer," narrow role of, 
54; cynical attitude towards, 
57; "developmental," 40-41; 
and "funny learning," 
126-27; and hierarchical 
ideology, 83; and internalized 
obstacles, 123-24; and "little 
schools," 215-17, 219, 221; 
negative attitudes towards, 
culturally shared, 57-58, 76; 
and pedagogy, 82; and 
Piaget's theory of stages, 138; 
and the potential for 
megachange, 55; "-proof 
computer systems, 76; and 
the quest for a science of 
education, 22-23; and the 
robotics workshop, 53; and 
strategies for change, 79-81; 
talents of, and progressive 
education, 14-15; and 
testing, 210; "time-traveling," 
1-2, 3-4; training of, 36, 
70-77; "true," and 
technicians, 55 
Technology Center (Silicon 

Valley), 78-79 
Temperature, 193-96 
Test(s), 2, 27, 47, 55, 104, 108, 
141; attitudes towards, and 
the real problem with our 
education system, 212; and 

Index • 241 

Bush's education plan, 

209- 10; and CAI programs, 
42, 165; and feedback, 

210- 11; and kitchen math, 
113; national system of, 
209-10; nervousness about, 
210; scores, international 
competition in, 209, 210, 

Thelma (case study), 43, 45-46, 
62, 64, 66-67, 213, 214 

Thermostats, 193-96 

Time-traveling teachers, 1-2, 

Tinker, Robert, 25 

Tools, 14-15, 161, 162 

Totalitarianism, 219 

Training, 36, 70-74, 76-77; use 
of the word, 70-71 

Transportation, 28-29 

Turing, Alan, 157 

Turkle, Sherry, 74, 131, 146-48, 
150, 180, 201 

Turtle, 31-32, 42, 127; and 
cybernetics, 185-91, 196-97, 
201-202, 203-205, 207; 
development of, 175-77, 
185-86; drawing a triangle 
with, 177-78; paths with 
commands, diagram of, 177. 
See also Logo 

Tutee, use of the term, 161-62 

Tutc use of the term, 161-62 

Twenty-one program, 170, 
173-75, 182 

Unconscious, 132, 152 
Uniformity, commitment to, 218 
University of Geneva, 168 

Values, 146, 217 
Victorian era, 89, 91 
Video games, ix, 9, 87, 140; 

appeal of, 4-5; first primitive, 

appearance of, 35 
Vulnerability, 91, 92, 94 
Vygotsky, Lev, 15 

Wall Street Journal, The, 37-38, 

Waves, 202-203 
Wiener, Norbert, 181-82, 184, 

Wilkins, John, 28 
Word processing, 70, 161 
World War II, 184, 185 
Wright, Orville, 15, 29, 86 
Wright, Wilbur, 15, 29, 86 
Writing. See Reading and 

Yearners, 1-21, 22-23, 162